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MECHANICAL DRAWING,

ELEMENTARY AND ADVANCED.

JOHN S. REID,

Instructor in Mechanical Drawing and Designing,
Armour Institute of Technology.

FOURTH EDITION, REVISED AND ENLARGED.
FIRST THOUSAND.

NEW YORK.

JOHN WILEY & SONS.

London : CHAPMAN & HALL, Limited.
1910

T^3

JOHN S. RE ID.

THE SCIENTIFIC PRESS

ROBERT DRUMMOND AND COMPANY

BROOKLYN, N. Y.

A2732C4

PREFACE TO THE FOURTH EDITION.

The third edition of " A Course in Mechanical Drawing "
was enlarged and improved by the addition of a set of concrete
problems, "A Course in Lettering " and "Present Practice in
Drafting Room Methods."

In this, the fourth edition, the work has been further enlarged
and improved by adding courses in Advanced Mechanical Draw-
ing consisting of short elementary courses in Advanced jsomet-
rical Drawing, Architectural Drawing, Sheet Metal Drafting,
Machine Details, and Working Drawings made from freehand
sketches of small machine parts.

This arrangement will preclude the necessity of using several
text-books in high schools, manual-training high schools, univer-
sity preparatory schools, technical colleges, and evening classes
where a variety of courses are given to meet the needs of students
preparing for different trades and professions.

With the addition of these new courses in advanced work it
has been thought desirable to change the title of the book from
"A Course in Mechanical Drawing " to " Mechanical Drawing,
Elementary and Advanced."

It was very gratifying to the writer to learn that the improve-
ments in the third edition were well received by both teachers
and students and it is hoped that the additions to the /fourth
edition will meet with a like approval.

John S. Reid.

PREFACE TO THE THIRD EDITION.

To meet the demands of high schools, manual training high
schools, university preparatory schools, technical colleges, and
evening classes, it has been found necessary to add to "A Course
in Mechanical Drawing" a concrete set of problems covering the
full requirements in mechanical drawing for entrance to the more
advanced classes in machine drawing, elementary machine de-
sign, and architectural drawing. The minimum time allowed
in a definite number of working hours for the finishing of each
plate, as introduced in this edition, is a new feature, and will be
much appreciated by Instructors when determining the amount
of work to require from their students in a given term. The
time allowed for the different plates has been carefully deter-
mined by taking note of the actual number of hours taken by
large numbers of students working on the same plates, under the
same conditions, and a conservative average taken, so that any
young man of fair intelligence and with an honest endeavor may
finish any of the plates in the time given.

The Course in Lettering, which has also been added to this
edition, will be found to be of great practical benefit to students
in all kinds of engineering drafting, and will be seen to embrace

vi PREFACE.

the most approved practice in drafting room methods at the
present time.

The report on the "Present Practice in Drafting Room
Methods," which will be found at the end of the book, is also
new, and will interest Instructors and enable them to adopt a
system in their drawing courses that may closely approximate the
best practice in the leading and most progressive drafting rooms
in the United States.

The thanks of the author are due and are most cordially

extended to those who have used this book in the past and have

encouraged and ass:isted him by gracious words and timely

suggestions.

John S. Reid.

Armour Institute of Technology.
Chicago, 111., September, 1908.

PREFACE.

In the course of a large experience as an instructor in
drawing and designing, the author of this work has often been
called upon to teach the elements of mechanical drawing to
students in marine, electrical, railway, and mechanical engi-
neering. Having tried and failed to find a book on the sub-
ject that was entirely suitable for his use as a text-book, he
has found it necessary to prepare the present work.

This course contains, in the author's judgment, a com-
plete and concise statement, accompanied by examples, of
the essential principles of mechanical drawing — all that any
young man of ordinary intelligence needs to master, by care-
ful study, the more advanced problems met with in machine
construction and design. Such works as the author has tried,
although most excellent from certain standpoints, were either
incomplete in some of the divisions of the subject or too volu-
minous and elementary in the treatment of details.

The author does not imagine this work is perfect, but he
believes that it comes nearer what is needed in teaching the
elements of mechanical drawing in technical schools, high
schools, evening drawing schools, and colleges than any work
he has examined.

The chapter on Conventions will be appreciated by students

Vlii PREFA CE.

when called upon to execute working drawings in practical

work. The methods described are considered by the author

to be those which have met with general approval by the

experienced American draftsmen of the present time.

My acknowledgments are due to E. C. Cleaves, professor

of drawing, Sibley College, Cornell University, for reading

the manuscript and making some valuable suggestions.

The Author.

April i, 1898.

CONTENTS

INTRODUCTION.

PAGE

The Complete Outfit, Illustrated i

CHAPTER I.

Instruments 7

Use of Instruments 7

Pencil 7

Drawing Pen g

Triangles n

T Square n

Drawing Board 11

Sibley College Scale 12

Scale Guard 12

Compasses 13

Dividers or Spacers 13

Spring Bows 14

Irregular Curves 14

Protractor 14

CHAPTER II.

Geometrical Drawing 16

CHAPTER III.

Conventions 56

CHAPTER IV.

Lettering and Figuring 64

X CONTENTS.

CHAPTER V.

Orthographic Projection 74

Shade Lines, Shades, and Shadows 103

Conventions 104

Shades ic6

Shadows 1 1 1

Isometrical Drawing 122

Working Drawings ' 129

Problems in Mechanical Drawing (Course I) „ 135

CHAPTER VI.
Architectural Drawing z^2

CHAPTER VII.
Architectural Design I75

CHAPTER VIII.
Sheet Metal Pattern Drafting 216

CHAPTER IX.

Elementary Machine Details, Including Screws, Nuts, Bolts, Keys,

Cotters and Gibs, Coupling Springs, etc 228

Problems in Mechanical Drawing (Course II) 277

Present Practice in Drafting Room Conventions and Methods in

Making Practical Working Drawings 289

MECHANICAL DRAWING.

INTRODUCTION.

A NEED has been felt by instructors and students, especially
in technical courses, for a text-book that would illustrate the
fundamental principles of mechanical drawing in such a prac-
tical, lucid, direct and progressive way as to enable the
instructor to teach, and the student to acquire, the greatest
number of the essential principles involved, and the ability to
apply them, in a draftsman-like manner, in the shortest space
of time.

With this in mind, the present work has been prepared
from the experience of the writer, a practical draftsman and
teacher for over fifteen years.

THE COMPLETE OUTFIT.

The outfit for students in mechanical and machine drawing
is as follows :

(i) The Drawing-board for academy and freshman work is
i6"X2i"x£", the same as that used for free-hand drawing.
The material should be soft pine and constructed as shown by
Fig. i.

(2) 1 Scribbling Pencil with rubber tip.

MECHANICAL DRAWING.

(3) Pencils, one 6H and one 4H Koh-i-noor or Faber.

(4) The T-Square; a plain pearwood T-square with a fixed
head is all that is necessary. Length 21".

Fig. i.

(5) Instruments. " Pocket Book" Set, shown by Fig. 2,
recommended as a first-class medium-priced set of instruments.
It contains

Fig. 2.

A Compass, 5}" long, with fixed needle-point, pencil, pen
and lengthening bar; a Spring Bow Pencil, 3" long; a
Spring Bow Pen, 3" long; a Spring Bow Spacer, 3" long;

INTRODUCTION.

2 Drawing-pens, medium and small, i Hair-spring Divider*
5" long; a nickel-plated box with leads.

Fig.

Fig. 4.

(6) A Triangular Boxwood Scale graduated as follows:
4" and 2", 3" and ij", 1" and J", f" and f", A" and A".

(7) 1 Triangle 3o°x6o°, celluloid, 10" long. Fig. 4.

1 " 45°, " 7" "

MECHA NIC A L DRA WING.

(8) i Irregular Curve. No. 13. Fig. 5.

(9) Emery Pencil Pointer.

(10) Ink, black waterproof. Fig. 7.

(11) Ink Eraser, Faber's Typewriter. No. 104.

(12) Pencil Eraser, "Emerald" No. 211. Fig. 9.

Fig.

Figs. 10, ii,

Fig. 7. Fig. 8.

(13) Sponge Rubber or Cube of "Artgum."

(14) Tacks, a small carton of 1 oz. copper tacks, and 1 doz.
small thumb tacks.

1 "

(15) Arkansas Oil Stone. 2/,Xi//XrV

(16) Protractor, German silver, about 5" diam.

(17) Scale Guard, " ". Fig. 13.

Fig. 12,

INTRODUCTION.

(18) 2 sheets of " Cream" Drawing Paper. [5"X2o'\
(iq) 2 " " Imperial Tracing Cloth. i$"X2q"0

(20) 1 Cross-section Pad. 8"Xio".

(21) 1 Scribbling Pad.

y§l|§§^

Fig. 10.

Fig. 11.

Fig. 12

(22) i Erasing Shield, nickel plated.

(23) 2 Lettering Pens, "Gillott" No. 303.

(24) 2 " " "Ball Point," No. 506.

(25) 2 " " " " No. 516.

(26) 1 Two-foot Rule.

CHAPTER I.
INSTRUMENTS.

It is a common belief among students that any kind of
cheap instrument will do with which to learn mechanical
drawing, and not until they have acquired the proper use of
the instruments should they spend money in buying a first-
class set. This is one of the greatest mistakes that can be
made. Many a student has been discouraged and disgusted
because, try as he would, he could not make a good drawing,
using a set of instruments with which it would be difficult for
even an experienced draftsman to make a creditable showing.

If it is necessary to economize in this direction it is better
and easier to get along with a fewer number, and have them
of the best, than \t is to have an elaborate outfit of question-
able quality.

The instruments shown in Fig. 2 are well made of a moderate
price, and with care and attention will give good satisfaction for
a long time.

USE OF INSTRUMENTS.

The Pencil. — Designs of all kinds are usually worked out

in pencil first, and if to be finished and kept they are inked in

and sometimes colored and shaded ; but if the drawing is only

to be finished in pencil, then all the lines except construction,

center, and dimension lines should be made broad and dark,

INSTRUMENTS. 7

so that the drawing will stand out clear and distinct. It will
be noticed that this calls for two kinds of pencil-lines, the
first a thin, even line made with a hard, fine-grained lead-
pencil, not less than 6H (either Koh-i-noor or Faber's), and
sharpened to a knife-edge in the following manner: The lead
should be carefully bared of the wood with a knife for about
\n ', and the wood neatly tapered back from that point ; then
lay the lead upon the emery-paper sharpener illustrated in the
outfit, and carefully rub to and fro until the pencil assumes a
long taper from the wood to the point ; now turn it over and
do the same with the other side, using toward the last a
slightly oscillating motion on both sides until the point has
assumed a sharp, thin, knife-edge endwise and an elliptical
contour the other way.

This point should then be polished on a piece of scrap
drawing-paper until the rough burr left by the emery-papei is
removed, leaving a smooth, keen, ideal pencil-point for draw-
ing straight lines.

With such a point but little pressure is required in the
hands of the draftsman to draw the most desirable line, one
that can be easily erased when necessary and inked in to
much better advantage than if the line had been made with a
blunt point, because, when the pencil-point is blunt the incli-
nation is to press hard upon it when drawing a line. This
forms a groove in the paper which makes it very difficult to
draw an even inked line.

The second kind of a pencil-line is the broad line, as
explained above ; it should be drawn with a somewhat softer
pencil, say 4H, and a thicker point.

All lines not necessary to explain the drawing should be

MECHA NIC A L DRA WI NG .

erased before inking or broadening the pencil-lines, so as to
make a minimum of erasing and cleaning after the drawing is
finished.

When drawing pencil-lines, the pencil should be held in a
plane passing through the edge of the T-square perpen-
dicular to the plane of the paper and making an angle with
the plane of the paper equal to about 6o°.

Lines should always be drawn from left to right. A soft
conical-pointed pencil should be used for lettering, figuring,
and all free-hand work.

The Draiving-pen. — The best form, in the writer's opinion,
is that shown in Fig. 14. The spring on the upper blade

Fig. 14.

Fig. 15.

spreads the blades sufficiently apart to allow for thorough
cleaning and sharpening. The hinged blade is therefore
unnecessary. The pen should be held in a plane passing
through the edge of the T-square at right angles to the plane
of the paper, and making an angle with the plane of the
paper ranging from 6o° to 900.

INSTRUMENTS. 9

The best of drawing-pens will in time wear dull on the
point, and until the student has learned from a competent
teacher how to sharpen his pens it would be better to have
them sharpened by the manufacturer.

It is difficult to explain the method of sharpening a draw-
ing-pen.

If one blade has worn shorter than the other, the blades
should be brought together by means of the thumb-screw, and
placing the pen in an upright position draw the point to and
fro on the oil-stone in a plane perpendicular to it, raising and
lowering the handle of the pen at the same time, to give the
proper curve to the point. The Arkansas oil-stones (No. 15
of " The Complete Outfit ") are best for this purpose.

The blades should next be opened slightly, and holding
the pen in the right hand in a nearly horizontal position, place
the lower blade on the stone and move it quickly to and fro,
slightly turning the pen with the fingers and elevating the
handle a little at the end of each stroke. Having ground the
lower blade a little, turn the pen completely over and grind
the upper blade in a similar manner for about the same length
of time ; then clean the blades and examine the extreme
points, and if there are still bright spots to be seen continue
the grinding until they entirely disappear, and finish the
sharpening by polishing on a piece of smooth leather.

The blades should not be too sharp, or they will cut the
paper. The grinding should be continued only as long as the
bright spots show on the points of the blades.

When inking, the pen should be held- in about the same
position as described for holding the pencil. Many drafts-
men hold the pen vertically. The position may be varied

10 MECHANICAL DRAWING.

with good results as the pen wears. Lines made with the pen
should only be drawn from left to right.

THE TRIANGLES.

The triangles shown at Fig. 4 (in il The Complete Outfit ")
are 10" and j" long respectively, and are made of transparent
celluloid. The black rubber triangles sometimes used are but
very little cheaper (about 10 cents) and soon become dirty
when in use; the rubber is brittle and more easily broken than
the celluloid.

Angles of 150, 750, 300, 450, 6o°, and 900 can readily be
drawn with the triangles and T-square. Lines parallel to
oblique lines on the drawing can be drawn with the triangles
by placing the edge representing the height of one of them
so as to coincide with the given line, then place the edge rep-
resenting the hypotenuse of the other against the corre-
sponding edge of the first, and by sliding the upper on the
lower when holding the lower firmly with the left hand any
number of lines may be drawn parallel to the given line.

The methods of drawing perpendicular lines and making
angles with other lines within the scope of the triangles and T-
square are so evident that further explanation is unnecessary.

THE T-SQUARE.
The use of the T-square is very simple, and is accom-
plished by holding the head firmly with the left hand against
the left-hand end of the drawing-board, leaving the right
hand free to use the pen or pencil in drawing the required
lines.

INSTRUMENTS. II

THE £>RAWING-BOARD.
If the left-hand edge of the drawing-board is straight and
rven and the paper is tacked down square with that edge and
Ihe T-square, then horizontal lines parallel to the upper edge
of the paper and perpendicular to the left-hand edge may be
drawn with the T-square, and lines perpendicular to these
can be made by means of the triangles, or set squares, as they
are sometimes called.

THE TRIANGULAR SCALE.

This scale, illustrated in Fig. 3 (in "The Complete Out-
fit"), was arranged to suit the needs of the students in machine
drawing, It is triangular and made of boxwood. The six
edges are graduated as follows; TV' or full size, z\f/, f"
and f" = 1 ft., 1" and \" = 1 ft., 3" and \\" = I ft., and
4" and 2" = 1 ft.

Drawings of very small objects are generally shown en-
larged— e.g., if it is determined to make a drawing twice the
full size of an object, then where the object measures one inch
the drawing would be made 2" ', etc.

Larger objects or small machine parts are often drawn full
size — i.e., the same size as the object really is — and the draw-
ing is said to be made to the scale of full size.

Large machines and large details are usually made to a
reduced scale — e.g., if a drawing is to be made to the scale of
2" = I ft., then 2" measured by the standard rule would be
divided into 12 equal parts and each part would represent 1".
See Fig. 8i£.

MECHANICAL DRAWING.

THE SCALE GUARD.

This instrument is shown in No. 17 (in "The Complete
Outfit "). It is employed to prevent the scale from turning,
so that the draftsman can use it without having to look for
the particular edge he needs every time he wants to Jay off
a measurement.

THE COMPASSES.

When about to draw a circle or an arc of a circle, take
hold of the compass at the joint with the thumb and two first
fingers, guide the needle-point into the center and set the
pencil or pen leg to the required radius, then move the thumb
and forefinger up to the small handle provided at the top of
the instrument, and beginning at the lowest point draw the
line clockwise. The weight of the compass will be the only
down pressure required.

Fig. 16.

The sharpening of the lead for the compasses is a very im-
portant matter, and cannot be emphasized too much. Before
commencing a drawing it pays well to take time to properly
sharpen the pencil and the lead for compasses and to keep
them always in good condition.

The directions for sharpening the compass leads are the
same as has already been given for the sharpening of the
straight-line pencil.

INSTRUMENTS.

THE DIVIDERS OR SPACERS.

This instrument should be held in the same manner as de-
scribed for the compass. It is very useful in laying off equal
distances on straight lines or circles. To divide a given line
into any number of equal parts with the dividers, say 12, it
is best to divide the line into three or four parts first, say 4,
and then when one of these parts has been subdivided accu-
rately into three equal parts, it will be a simple matter to
step off these latter divisions on the remaining three-fourths

Fig. 17.

of the given line. Care should be taken not to make holes in
the paper with the spacers, as it is difficult to ink over them
without blotting.

THE SPRING BOWS.

These instruments are valuable for drawing the small cir-
cles and arcs of circles. It is very important that all the

14 MECHANICAL DRAWING.

small arcs, such as fillets, round corners, etc., should be care-
fully pencilled in before beginning to ink a drawing. Many
good drawings are spoiled because of the bad joints between
small arcs and straight lines.

When commencing to ink a drawing, all small arcs and
small circles should be inked first, then the larger arcs and
circles, and the straight lines last. This is best, because it is
much easier to know where to stop the arc line, and to draw
the straight line tangent to it, than vice versa.

IRREGULAR CURVES.

The irregular curve shown in Fig. 5 is useful for draw-
ing irregular curves through points that have already been
found by construction, such as ellipses, cycloids epicyloids, etc.,
as in the cases of gear-teeth, cam outlines, rotary pump wheels,
etc.

When using these curves, that curve should be selected
that will coincide with the greatest number of points on the
line required.

THE PROTRACTOR.

This instrument is for measuring and constructing angles.
It is shown in Fig. 12. It is used as follows when measuring
an angle: Place the lower straight edge on the straight line
which forms one of the sides of the angle, with the nick
exactly on the point of the angle to be measured. Then the
number of degrees contained in the angle may be read from
the left, clockwise.

In constructing an angle, place the nick at the point from
which it is desired to draw the angle, and on the outer circum-

INSTR UMEN TS. 1 5

ference of the protractor, find the figure corresponding to the
number of degrees in the required angle, and mark a point on
the paper as close as possible to the figure on the protractor;
after removing the protractor, draw a line through this point
to the nick, which will give the required angle.

CHAPTER II.
GEOMETRICAL DRAWING.

The following problems are given to serve a double pur-
pose : to teach the use of drawing instruments, and to point
out those problems in practical geometry that are most useful
in mechanical drawing, and to impress them upon the mind of
the student so that he may readily apply them in practice.

The drawing-paper for this work should be divided tem-
porarily, with light pencil-lines, into as many squares and rec-
tangles as may be directed by the instructor, and the drawings
made as large as the size of the squares will permit. The
average size of the squares should be not less than 4". When
a sheet of drawings is finished these boundary lines may be
erased.

It will be noticed in the illustrations of this chapter that
all construction lines are made very narrow, and given and
required lines quite broad. This is sufficient to distinguish
them, and employs less time than would be necessary if the
construction lines were made broken, as is often the case.

If time will permit, it is advisable to ink in some of these

drawings toward the last. In that event, the given lines may

be red, the construction lines blue, and the required lines

black.

But even when inked in in black, the broad and narrow

GEOMETRICAL DRAWING. I J

lines would serve the purpose very well without the use of col-
ored inks.

The principal thing to be aimed at in making these draw-
ings is accuracy of construction. All dimensions should be
laid off carefully, correctly, and quickly. Straight lines join-
ing arcs should be exactly tangent, so that the joints cannot
be noticed. It is the little things like these that make or mar
a drawing, and if attended to or neglected they will make or
mar the draftsman. The constant endeavor of the student
should be to make every drawing he begins more accurate,
quicker and better in every way than the preceding one.

A drawing should never be handed in as finished until the
student is perfectly sure that he cannot improve it in any way
whatever, for the act of handing in a drawing is the same, or
should be the same, as saying This is the best that I can do;
I cannot improve it ; it is a true measure of my ability to
make this drawing.

If these suggestions are faithfully followed throughout this
course, success awaits any one who earnestly desires it.

Fig.bi8. To BlSECT A Finite Straight Line. — With
A and B in turn as centers, and a radius greater than the half
of ABy draw arcs intersecting at E and F. Join EF bisect-
ing AB at C.

An arc of a circle may be bisected in the same way.

pfgbii; To Erect a Perpendicular at the End of
THE Line. — Assume the points above the line as center and
radius EB describe an arc CBD cutting the line AB in the
point C. From C draw a line through E cutting the arc in
D. Draw DB the perpendicular.

Fi^'ao! The Same Problem: a Second Method. —

MECHANICAL DRAWING.

With center B and any radius as BC describe an arc CDE
with the same radius; measure off the arcs CDa.nd DE. With
D and E as centers and any convenient radius describe arcs in-
tersecting at F. FB is the required perpendicular.
'e

Fig. 21.

FiS^i*. To Draw a Perpendicular to a Line
from a Point above or below It. — Assume the point
C above the line. With center C and any suitable radius
cut the line AB in E and F. From E and F describe'arcs
cutting in D. Draw CD the perpendicular required.

GE OME 7 RICA L DRA WIN G.

Fi2,b*22; To Bisect A Given Angle. — With A as center
and any convenient radius describe the arc BC. With B and
C as centers and any convenient radius draw arcs intersecting
at D. Join AD, then angle BAD = angle DAC.

Fig. 22.

Fi^bf] To Draw a Line Parallel to a Given
Line AB Through a Given Point C. — From any point
on AB as B with radius BC describe an arc cutting AB in A,
From C with the same radius describe arc BD. From B with
AC as radius cut arc BD in D. Draw CD. Line CD is paral-
lel to AB.

J?. T\ 1 2)

Fig. 23.

Pi^aJ; From a Point D on the Line DE to set
off an Angle equal to the given Angle BAC. — From

MECHANICAL DRAWING.

A with any convenient radius describe arc BC. From D wit
the same radius describe arc EF. With center E and radius
BC cut arc EF in F. Join DF. Angle EDF is = angle BAC.

Fig. 24.

FiS.b25.' • To Divide an Angle into two equal
Parts, when the Lines do not Extend to a Meeting
Point. — Draw the line CD and CE parallel and at equal dis-

Fig. 25.

tances from the lines AB and FG. With C as center and any
radius draw arcs 1,2. With 1 and 2 as centers and any con-

GEOMETRICAL DRAWIXG. 21

venient radius describe arcs intersecting at//". A line through
C and H divides the angle into two equal parts.

Fi2b'2(3*. To Construct a Rhomboid having Adja-
cent Sides equal to two Given Lines AB and AC, and
an Angle equal to a Given Angle A. — Draw line DE
equal to AD. Make D — angle A. Make DF — AC. From
F with line AB as radius and from E with line AC as radius
describe arcs cutting in G. Join FG and EG.

Fi"gb' 27*. To DlvIDE THE LlXE AB into any Number
OF EQUAL Parts, SAY 15. — Draw a line CD parallel to AB,
of any convenient length. From C set off along this line the
number of equal parts into which the lineABis to be divided.
Draw CA and DB and produce them until they intersect at
E. Through each one of the points 1, 2, 3, 4, etc., draw
lines to the point E, dividing the line AB into the required
number of equal parts.

This problem is useful in dividing a line when the point
required is difficult to find accurately — e.g., in Fig. 28 AB is
the pitch of the spur gear, partly shown, which includes a

MECHANICAL DRAWING.

space and a tooth and is measured on the pitch circle. In
cast gears the space is made larger than the thickness of the
tooth, the proportion being about 6 to 5 — i.e., if we divide
the pitch into eleven equal parts the space will measure T6T

»cP^

q 1 & 3 4 S 6 7 89 1.011 1213 U J>
Fig. 27.

Fig

and the tooth T5T. The T*T which the space is larger than the
tooth is called the backlash. Let A'B' be the pitch chord of
the arc AB. Draw CD parallel to A'B' at any convenient
distance and set off on it 1 x. equal spaces of any convenient
length. Draw CA' and DB' intersecting at E. From point
5 draw a line to E which will divide A'B' as required; the
one part yV and the other T6T.

Fi2.b' 2^ To DlvIDE A Given Line into any Number
of Equal Parts: Another Method. — Let AB be the
given line. From A draw A C at any angle, and lay off on it
the required number of equal spaces of any convenient length.
Join CB and through the divisions on AC draw lines parallel
to CB, dividing AB as required in the points i', 2', 3', 4', etc.

Mg.b" 30." To Divide a Line AB Proportionally to
the Divided Line CD. — Draw AB parallel to CD at any

GEOMETRICAL DRAWING.

distance from it. Draw lines through CA and DB and produce
them till they meet at E. Draw lines from E through the
divisions I, 2, 3, 4, etc., of line CD, cutting line AB in the

a l

3 4 5 6 7 S 9 10 111213 U g
Fig. 29.

points 5, 6, 7, 8, etc. The divisions on AB will have the
same proportion to the divisions on CD that the whole line
AB has to the whole line CD — i.e., the lines will be propor-
tionally divided.

Fi^' 31I The Same : Another Method. — Let BC,
the divided line, make any angle with BA, the line to be di-

MECHANICAL DRAWING.

vided at B. Draw line CA joining the two ends of the lines.
Draw lines from 5, 6, 7, 8, parallel to CA, dividing line AB
in points 1, 2, 3, 4, proportional to BC

Ffg.b* 32! To Construct an Equilateral Triangle
on A Given Base AB, — From the points A and B with AB
as radius describe arcs cutting in C. Draw lines AC and BC.
The triangle ABC is equilateral and equiangular.

Fig. 32.

Mgb* 33. To Construct an Equilateral Triangle
of a Given Altitude, AB. — From both ends of AB draw
lines perpendicular to it as CA and DB. From A with any
radius describe a semicircle on CA and with its radius cut off
arcs 1, 2. Draw lines from A through 1, 2, and produce
them until they cut the base BD.

Ffgb*34. To Trisect a Right Angle ABC— From
the angular point B with any convenient radius describe an
arc cutting the sides of the angle in C and A. From C and A
with the same radius cut off arcs 1 and 2. Draw lines \B and
2B, and the right angle will be trisected.

GEOMETRICAL DRAWING.

Fig.b* 35! To Construct any Triangle, its Three
Sides AB and £7 being given. — From one end of the base
as A describe an arc with the line B as radius. From the
other end with line C as radius describe an arc, cutting the
first arc in D. From D draw lines to the ends of line A, and a
triangle will be constructed having its sides equal to the sides
given. To construct any triangle the two shorter sides B and
C must together be more than equal to the largest side A.

Fig. 34.

Fig. 35.

Fig. 36.

Fig. 37.

Ffgb' si! To Construct a Square, its Base AB
Erect a perpendicular at B. Make BC equal

Fig. 36

BEING GIVEN

MECHANICAL DRAWING.

to AB. From A and C with radius AB describe arcs cutting
in D. Join DC and DA.

Fi*gb* 37.' To Construct a Square, given its Di-
agonal AB. — Bisect AB in C. Draw Z)/7 perpendicular to
AB at C Make CD and £F each equal to CA. Join y2Z?,
£>j5, BF, and FA.

Fig.b* is! To Construct a Regular Polygon of any
Number of Sides, the Circumscribing Circle being
GIVEN. — At any point of contact, as C} draw a tangent AB
to the given circle. From C with any radius describe a semi-
circle cutting the given circle. Divide the semicircle into as
many equal parts as the polygon is required to have sides, as
I, 2, 3, 4, 5, 6. Draw lines from C through each division,
cutting the circle in points which will give the angles of the
polygon.

Fi2b' io! Another Method. — Draw a diameter AB of
the given circle. Divide AB into as many equal parts as
the polygon is to have sides, say 5. From A and B with the

GEOMETRICAL DRAWING.

line AB as radius describe arcs cutting in C, draw a line from
C through the second division of the diameter and produce it
cutting the circle in D. BD will be the side of the required
polygon. The line C must always be drawn through the
second division of the diameter, whatever the number of
sides of the polygon.

Fi£b' to.' To Construct any Regular Polygon
with A GIVEN Side AB.— Make BD perpendicular and
equal to AB. With B as center and radius AB describe arc
DA. Divide arc DA into as many equal parts as there are
sides in the required polygon, as 1, 2, 3, 4, 5. Draw B2.
Bisect line AB and erect a perpendicular at the bisection cut-
ting B2 in C. With C as center and radius CB describe a
circle. With AB as a chord step off the remaining sides of
the polygon.

Fig. 40.

Fig. 41.

Firgb'fi: Another Method.— Extend line AB. With
center A and any convenient radius describe a semicircle.
Divide the semicircle into as many equal parts as there are
sides in the required polygon, say 6. Draw lines through
every division except the first. With A as center and AB as

28 MECHANICAL DRAWING.

radius cut off A2 in C. From C with the same radius cut A3
in D. From D, A\ in E. From B, A$ in F. Join AC, CD,
DE, EF, and FB.

Ffgb' ft.' To Construct a Regular Heptagon, the
Circumscribing Circle being given. — Draw a radius AB.
With i? as center and BA as radius, cut the circumference in
1,2; it will be bisected by the radius in C. Ci or C2 is equal
to the side of the required heptagon.

Fig. 42.

Ffs.b* 43 To Construct a Regular Octagon, the
Circumscribing Circle being given. — Draw a diameter
AB. Bisect the arcs AB in C and D. Bisect arcs CA and
CB in 1 and 2. Draw lines from 1 and 2 through the center
of the circle, cutting the circumference in 3 and 4. Join A\,
iC, C2, 2£t i?3, etc.

Ffgb* U To Construct a Pentagon, the Side AB
BEING GIVEN. — Produce AB. With B as center and BA as
radius, describe arc AD2. With center A and same radius,
describe an arc cutting the first arc in D. Bisect AB in E.

GEOMETRICAL DRAWING.

Draw line DE. Bisect arc BD in F. Draw line EF. With
center C and radius EF cut off arc C\ and 1, 2 on the semi-
circle. Draw line B2 ; it will be a second side of the penta-

gon. Bisect it and draw a line perpendicular to it at the
bisection. The perpendiculars from the sides AB and B2
will cut in G. With G as center and radius GA describe a
circle • it will contain the pentagon.

Fig. 45.

3°

MECHANICAL DRAWING.

^2h' 51' To Construct a Heptagon on a Given

.rig. 4:0.

LINE AB. — Extend line AB to C. From B with radius AB
describe a semicircle. With center A and same radius de-
scribe an arc cutting the semicircle in D. Bisect AB in E.
Draw line DE. With C as center and DE as radius, cut off
arc I on the semicircle. Draw line B\ ; it is a second side of
the heptagon. Bisect it and obtain the center of the circum-
scribing circle as in the preceding problem.

Fig*.15' Hi To Inscribe an Octagon in a Given
Square. — Draw diagonals AD, CB intersecting at O. From
A, B, C, and D with radius equal to AO describe quadrants
cutting the sides of the square in I, 2, 3, 4, 5, 6, 7, 8. Join
these points and the octagon will be inscribed.

< >

f \

Fig. 46.

Fig. 47-

Fig.b* I?.' To Construct a Regular Octagon on a
Given Line AB. — Extend line AB in both directions. Erect
perpendiculars at A and B. With centers A and B and radius
AB describe the semicircle CEB and AF2. Bisect the quad-
rants CE and DF in 1 and 2, then A\ and B2 will be two
more sides of the octagon. At 1 and 2 erect perpendiculars
1. 3 and 2, 4 equal to AB. Draw 1-2 and 3-4. Make the

GEOMETRICAL DRAWING.

perpendiculars at A and B equal to I -2 or 3-4 — viz., A$ and
i>6. Complete the octagon by drawing 3-5, 5-6, and 6-4.

Fi-b' ±s. To Draw a Right Line Equal to Half
THE ClRCUxMFERENCE OF A Given CIRCLE. — Draw a diam-
eter AB. Draw line AC perpendicular to AB and equal to
three times the radius of the circle. Draw another perpen-
dicular at B to AB. With center B and radius of the circle
cut off arc BD, bisect it and draw a line from the center of
the circle through the bisection, cutting line B in E. Join
EC. Line EC will be equal to half the circumference of
circle A.

. G
A c

Figb" 49'. To Find A Mean Proportional to two
Given Right Lines. — Extend the line AB to E making BE
equal to CD. Bisect AE in F. From F with radius FA de-
scribe a semicircle. At B where the two given lines are
joined erect a perpendicular to AE cutting the semicircle in
G. BG will be a mean proportional to CD and AB.

Fi|b' io. To FlND A Third Proportional (less) to
two Given Right Lines AB and CD. — Make EF= the
given line AB. Draw EG '= DC making an angle with EF.
Join FG. From E with EG as radius cut EF in H. Draw

MECHANICAL DRAWING.

H parallel to FG, cutting EG in /. EI is the third propor-
tional (less) to the two given lines.

Fig. 50.

Fig. 51.

Fi2.b* ii! To Find a Fourth Proportional to three
Given Right Lines AB, CD, and EF.— Make ^^=the
given line AB. Draw GI = CD, making any convenient
angle to GH. Join HI. From G lay off GK = EF. From
K draw a parallel to HI cutting GI in L. GL is the fourth
proportional required.

Fig. 53.

Fi£b §2! To Find the Center of a Given Arc ABC.
— Draw the chords AB and CD and bisect them. Extend
the bisection lines to intersect in D the center required.

GEOMETRICAL DRAWING.

Figb* 53.' To Draw a Line Tangent to an Arc of a
CIRCLE. — (ist.) When the center is not accessible. Let B
be the point through which the tangent is to be drawn.
From B lay off equal distances as BE, BF. Join EF and
through B draw ABC parallel to EF. (2d.) When the cen-
ter D is given. Draw BD and through B draw ABC perpen-
dicular to BD. ABC is tangent to the circle at the point B.

mgh' IS.' To Draw Tangents to the Circle C from
THE POINTS WITHOUT It. — Draw^C and bisect it in E.
From E with radius EC describe an arc cutting circle C in B
and D. Join CB, CD. Draw AB and AD tangent to the
circle C.

Fig. 54. Fig. 55.

Firg.b* 55! To Draw a Tangent between two Cir-
cles.— -Join the centers A and B. Draw any radial line
from A as A2 and make 1-2 = the radius of circle B. From
A with radius A-2 describe a circle C2D. From center B

MECHANICAL DRAWING.

draw tangents BC and BD to circle C2D at the points C and
D by preceding problem. Join AC and ^4Z? and through
the points E and F draw parallels FG and EH to BD and i?C.
/^ and EH are the tangents required.

Fi^' IS: To Draw Tangents to two Given Cir-
cles A AND B.— Join ^ and B. From ^4 with, a radius
equal to the difference of the radii of the given circles de-

Fig. 56.

scribe a circle GF. From B draw the tangents BF and BGy
by Prob. 37. Draw AF and ^4£ extended to E and //.
Through ii and H draw i:C and HD parallel to BF and BG
respectively. EC and Z?77 are the tangents required.

^' I?; To Draw an Arc of a Circle of Given
Radius Tangent to two Straight Lines. — AB and AC
are the two straight lines, and r the given radius. At a dis-
tance = r draw parallels 1-2 and 3-4 to AC and ^4Z?, inter-

GEOMETRICAL DRAWING.

secting at F. From F draw perpendiculars FD and FE.
With F as center and FD or FE as radius describe the re-
quired arc, which will be tangent to the two straight lines at
the points D and E.

Fi*£b' 5^; To Draw an Arc of a Circle Tangent
to two Straight Lines BC and CD when the Mid-
position G IS GIVEN. — Draw CA the bisection of the angle
BCD and EF at right angles to it through the given point G.
Next bisect either of the angles FEB or EFD. The bisection
line will intersect the central line CA at A, which will be the
center of the arc. From A draw perpendiculars Ai and A2,
and with either as a radius and A as center describe an arc
which will be tangent to the lines BC and CD at the points I
and 2.

fJ>A

Fig. 58.

Fig?' 59'. To Inscribe a Circle within a Triangle
ABC. — Bisect the angles A and B. The bisectors will meet
in D. Draw Di perpendicular to AB. Then with center D
and radius = D\ describe a circle which will be tangent to
the given triangle at the points I, 2, 3.

Ffgb* to'. To Draw an Arc of a Circle of Given
Radius R tangent to two Given Circles A and B. —
From A and B draw any radial lines as A$, B\. Outside
the circumference of each circle cut off distances 1-3 and 2-4

MECHANICAL DRAWING.

each =z the given radius R. Then with center A and radius
A— 3, and center B and radius £-4 describe arcs intersecting at
C. Draw CA,CB cutting the circles at 5 and 6. With centre
C and radius C$ or C6 describe an arc which will be tangent
at points 5 and 6.

Prob. 43.
Fig. 61.

Fig. 60.

To Draw an Arc of a Circle of Given

Radius R tangent to two Given Circles A and B

when the Arc includes the Circles. — Through A and B
draw convenient diameters and extend them indefinitely. On

GEOMETRICAL DRAWING.

these measure off the distances 1-2 and 3-4, each equal in
length to the given radius R. Then with center A and radius
A2y center B and radius £4, describe arcs cutting at C. From
C draw £~5 and C6 through B and A. With center C and ra-
dius C6 or C$ describe the arc 6, 5, which will be tangent to
the circles at the points 6 and 5.

Fi?' 62! To Draw an Arc of a Circle of Given
Radius R tangent to Two Given Circles A and B
when the Arc includes one Circle and excludes the
OTHER. — Through A draw any diameter and make 1-2 = R.

Fig. 62.

From B draw any radius and extend it, making 3-4 = R. With
center A and radius A2 and center B and radius B4 describe
arcs cutting at C. With C as center and radius = C$ or C6
describe the arc 5, 6.

Fi|b' 63! Draw an Arc of a Circle of Given Ra-
dius R tangent to a Straight Line AB and a Circle
CD. — From £, the center of the given circle, draw an arc of a

3° MECHANICAL DRAWING.

circle i , 2 concentric with CD at a distance R from it, and
also a straight line 3, 4 parallel to AB at the same distance R
from ^4i?. Draw £(2 intersecting CD at 5. Draw the perpen-
dicular 06. With center O and radius (96 or 0$ describe the
required arc.

Fig. 63.

FiJb' 64*. To Describe an Ellipse Approximately
BY MEANS OF THREE RADII (F. R. Honey's method). —

Fig. 64.

Draw straight lines RH and //<2> making any convenient angle
at H. With center /f and radii equal to the semi-minor and

GEOMETRICAL DRAWING.

semi-major axes respectively, describe arcs LM and NO. Join

LO and draw MK and NP parallel to LO. Lay off Zi = J

of ZAr. Join <9i and draw M2 and ^3 parallel to Oi. Take

//3 for the longest radius (= T), H2 for the shortest radius

(= E), and one-half the sum of the semi-axes for the third

radius (= S), and use these radii to describe the ellipse as

follows: Let AB and CD be the major and minor axes. Lay

off AAr = E and A^ = 5. Then lay off CG = T and C6 = 5.

With £ as center and G6 as radius draw the arc 6, g. With

center 4 and radius 4, 5, draw arc 5, g, intersecting 6, ^ at g.

Draw the line Gg and produce it making £8 = T. Draw g,

4 and extend it to 7 making g, 7 = S. With center G and

radius GC(=T) draw the arc CS. With center £- and radius

gy 8 ( = 5) draw the arc 8, 7. With center 4 and radius 4, 7

(=E) draw arc 7^4. The remaining quadrants can be drawn

in the same way.

Fi2b* 65 To Draw ax Ellipse having given the

Axes AB AND CD. — Draw AB and CD at right angles to and

bisecting each other at E. With center C and radius EA cut

AB in F and F the foci. Divide EF or EF' into a number of

parts as shown at 1, 2, 3, 4, etc. Then with F and F' as cen-
c

Fig. 65.

Fig. 67.

ters and ^4 1 and 2?i, and ^2 and ^2, etc., as radii describe arcs
intersecting in i£, 5, etc., until a sufficient number of points

MECHANICAL DRAWING.

are found to draw the elliptic curve accurately throughout.
(No. 5 of the "Sibley College Set" of irregular curves is
very useful in drawing this curve.) To draw a tangent to
the ellipse at the point G: Extend FG and draw the bisector
of the angle HGF' ' . KG is the tangent required.

pfg.b' el; Another Method.— Let AB and AC be the
semi axes. With A as center and radii AB and AC describe
circles. Draw any radii as Al and A4., etc. Make 3 1, 42,
etc., perpendicular to AB, and Z>2, E$, etc., parallel to AB.
Then 1, 2, 5, etc., are points on the curve.

Figb* 6?'. Another Method. — Place the diameters as
before, and construct the rectangle CDEF. Divide AB and
DB and BF into the same number of equal parts as 1, 2, 3 and
B. Draw from C through points 1, 2, 3 on AB and BD
lines to meet others drawn from E through points 1, 2, 3 on
AB and FB intersecting in points GHK. GHK are points on
the curve.

Fi*gb' Is! Another Method.— Place the diameters AB
and CD as shown in Drawing No. 1. Draw any convenient
■1 ■

>L ,K

Fig. 68.

angle RHQ, Drawing No. 2. With center //"and radii equal
to the semi-minor and semi-major axes describe arcs LM and-

GEOMETRICAL DRAWING. 4 1

NO. Join LO and draw MK and NP parallel to LO. Then
from C and Z> with a distance = ///* lay off the points I 1'on
the minor axis and from A and B with a distance = HK lay
off the points 2 2' on the major axis. With centers l,l', 2 and
2' and radii i-Z> and 2/-2?, respectively, draw arcs of circles.
On a piece of transparent celluloid 7Tay off from the point G,
GF and GE = the semi-minor and semi-major axes respec-
tively. Place the point ^on the major axis and the point E on
the minor axis. If the strip of celluloid is now moved over
the figure, so that the point E is always in contact with the
semi-minor axis and the point F with the semi major axis, the
necessary number of points may be marked through a small
hole in the celluloid at G with a sharp conical-pointed pencil,
and thus complete the curve of the ellipse between the arcs of
circles.

FfSb' I9! To Construct a Parabola, the Base CD
and the Abscissa AB being given. — Draw EF through A
parallel to CD and CE and DF parallel to AB. Divide AE,
AF, EC, and FD into the same number of equal parts.
Through the points 1, 2, 3 on AF and AE draw lines parallel
to AB, and through A draw lines to the points 1,2, 3 on FD
and EC intersecting the parallel lines in points 4, 5, 6, etc., of
the curve.

Fr2b' f §; Given the Directrix BD and the Focus C
to Draw a Parabola and a Tangent to It at the Point
3. — The parabola is a curve such that every point in the curve
is equally distant from the directrix BD and the focus C. The
vertix E is equally distant from the directrix and the focus,
i.e. CE is = EB. Any line parallel to the axis is a diameter.
A straight line drawn across the figure at right angles to the

MECHANICAL DRAWING.

axis is a double ordinate, and either half of it is an ordinate.
The distance from C to any point upon the curve, as 2 is
always equal to the horizontal distance from that point to the
directrix. Thus Ci = i, i' , C2 to 2, 2', etc. Through C
draw ACF at right angles to BD, ACF is the axis of the

Ai 2 3 F

t£

B '>

Fig. 70.

curve. Draw parallels to BD through any points in AB, and
with center C and radii equal to the horizontal distances of
these parallels from BD describe arcs cutting in the points I,
2, 3, 4, etc. These are points in the curve. The tangent to
the curve at the point 3 may be drawn as follows : Produce
AB to F. Make EF = the horizontal distance of ordinate 33
from E. Draw the tangent through $F.

FiJb* 71! To Draw an Hyperbola, having given
the Diameter AB, the Abscissa BD, and Double Ordi-
nate EF. — Make F4 parallel and equal to BD. Divide DF
and F4 into the same number of equal parts. From B draw
lines to the points in 4F and from A draw lines to the points
in DF. Draw the curve through the points where the lines
correspondingly numbered intersect each other.

GEOMETRICAL DRAWING.

F?gb' ?** To Construct an Oval the Width AB

72.

BEING GIVEN. — Bisect AB by the line CD in the point E,
and with E as center and radius EA draw a circle cutting CD in

Fig. 71.

Fig. 72.

F. From ^4 and i> draw lines through F. From A and B with
radius equal to AB draw arcs cutting the last two lines in G
and H. From F with radius /l7 describe the arc 67/ to meet
the arcs AG and BH, which will complete the oval.

fTS!5' 73! GlVEN AN Ellipse to Find the Axes and
Foci. — Draw two parallel chords AB and CD. Bisect each
of these in E and F. Draw EF touching the ellipse in 1 and
2. This line divides the ellipse obliquely into equal parts.
Bisect I, 2 in G, which will be the center of the ellipse. From
G with any radius draw a circle cutting the ellipse in HIJK.
Join these four points and a rectangle will be formed in the
ellipse. Lines LM and NO, bisecting the sides of the
rectangle, will be the diameters or axes of the ellipse. With
N or O as centers and radius = GL the semi-major axis, de-
scribe arcs cutting the major axis in P and Q the foci.

m^' 74'. To Construct a Spiral of one Revolu-
tion.— Describe a circle using the widest limit of the spiral as

MECHANICAL DRAWING.

a radius. Divide the circle into any number of equal parts as
A, B, Cj etc. Divide the radius into the same number of equal
parts as I to 12. From the center with radius 12, 1 describe
an arc cutting the radial line B in i'. From the center con-
tinue to draw arcs from points 2, 3, 4, etc., cutting the corre-
sponding radii C, D, B, etc. in the points 2', 3', 4', etc. From
12 trace the Archimedes Spiral of one revolution.

Fi^' 75. To Describe a Spiral of any Number of
REVOLUTIONS, E.G., 2. — Divide the circle into any num-
ber of equal parts as A, B, C, etc., and draw radii. Divide
the radius A 12 into a number of equal parts corresponding
with the required number of revolutions and divide these
into the same number of equal parts as there are radii, viz.,
1 to 12. It will be evident that the figure consists of two
separate spirals, one from the center of the circle to 12, and
one from 12 to A. Commence as in the last problem, draw-
ing arcs from I, 2, 3, etc., to the correspondingly numbered
radii, thus obtaining the points marked 1', 2', 3', etc. The
first revolution completed, proceed in the same manner to
find the points 1", 2" , 3", etc. Through these points trace
the spiral of two revolutions.

GEOMETRICAL DRAWING.

Fir2b' I?.' To Construct the Involute of the Cir-
cle 0. — Divide the circle into any number of equal parts
and draw radii. Draw tangents at right angles to these radii.
On the tangent to radius I lay off a distance equal to one
of the parts into which the circle is divided, and on each of

the tangents set off the number of parts corresponding to the
number of the radii. Tangent 12 will then be the circumfer-
ence of the circle unrolled, and the curve drawn through the
extremities of the other tangents will be the involute.

E[°b- 52* To Describe an Ionic Volute. — Divide the

r iff. * * •

given height into seven equal parts, and through the point 3
the upper extremity of the third division draw 3, 3 perpen-
dicular to AB. From any convenient point on 33 as a cen-
ter, with radius equal to one-half of one of the divisions on
AB, describe the eye of the volute NPNM, shown enlarged
at Drawing No. 2. NN corresponds to line 3, 3, Drawing
No. 1. Make PM perpendicular to NN and inscribe the
square NPNM, bisect its sides and draw the square 11, 12,

MECHANICAL DRA\

13, 14. Draw the diagonals 11, 13 and 12, 14 and divide
them as shown in Drawing No. 2. At the intersections of
the horizontal with the perpendicular full lines locate the
points 1, 2, 3, 4, etc., which will be the centers of the quad-
rants of the outer curve. The centers for the inner curve
will be found at the intersections of the horizontal and per-

/ 1

/JVc

,2.

\l2 \

' n —

7/\

—

x]/

1 vH

yff\

\hY

\jj<

y~5

■ \\i

>lz 1

\ lc

U /

M
Fig. 77-

pendicular broken lines, drawn through the divisions on the
diagonals. Then with center 1 and radius iP draw arc FN,
and with center 2 and radius 2N draw arc NMy with center 3
and radius 3 M draw arc ML, etc. The inner curve is drawn
in a similar way, by using the points on the diagonals indi-
cated by the broken lines as centers.

mgh' ?»: To Describe the Cycloid.— AB is the di-
rector, CB the generating circle, X a piece of thin transparent
celluloid, with one side dull on which to draw the circle C.
At any point on the circle C puncture a small hole with a
sharp needle, and place the point C tangent to the director
AB at the point from which the curve is to be drawn. Hold
the celluloid at this point with a needle, and rotate it until

GEOMETRICAL DRAWING.

the arc of the circle C intersects the director AB. Through
the point of intersection stick another needle and rotate X
until the circle is again tangent to AB, and through the punc-
ture at C with a 4H pencil, sharpened to a fine conical point,
mark the first point on the curve. So proceed until sufficient
points have been found to complete the curve.

(NOTE. — The thin celluloid was first used as a drawing
instrument by Professor H. D. Williams, of Sibley College,
Cornell University.)

Ffgb' 79. To Find the Length of a Given Arc of a
CIRCLE APPROXIMATELY. — Let BC be the given arc. Draw
its chord and produce it to A, making BA equal half the

Fig. 78.

Fig. 79.

chord. With center A and radius AC describe arc CD cut-
ting the tangent line BD at £>, and making it equal to the
arc BC.

Figb* so! To Describe the Cycloid by the Old
Method. — Divide the director and the generating circle into
the same number of equal parts. Through the center a draw
ag parallel to AB for the line of centers, and divide it as AB
in the points £, c, d, e, f, and g. With centers/, e, d, etc., de-
scribe arcs tangent to AB, and through the points of division
on the generating circle 1,2, 3, etc., draw lines parallel to

MECHANICAL DRAWING.

AB cutting the arcs in the points i', 2', 3', etc. These will be
points in the curve.

An approximate curve may be drawn by arcs of circles.
Thus, taking/' as center and f'g' as radius, draw arc g'l'.

Fig. 80.

Produce \'f and 2' e' until they meet at the center of the
second arc 2ff, etc.

To Describe the Epicycloid and the

Prob. 63.
Fig. 81.

HYPOCYCLOID. — Divide the generating circle into any num-
ber of equal parts, 1, 2, 3, etc., and set off these lengths from
C on the directing circle CB as e' ', d\ c' , etc. From A the cen-
ter of the directing circle draw lines through e\ d' , c , etc., cut-
ting the circles of centers in e, d, c, etc. From each of these
points as centers describe arcs tangent to the directing circle.
From center A draw arcs through the points of division on
the generating circle, cutting the arcs of the generating circles
in their several positions at the points i', 2' , 3', etc. These
will be points in the curve.

&?*• ||; Another Method. — Draw the generating
circle on the celluloid and roll it on the outside of the gener-
ating circle BC for the Epicycloid, and on the inside for the

GEOMETRICAL DRAWING.

Hypocycloid, marking the points in the curve 1,2, 3, etc., in
similar manner to that described for the Cycloid.

Fig. 82.

Fig. 81.

Fig. 83.

F$.b'!!; To Draw THE ClSSOlD.— Draw any line AB
and BC perpendicular to it. On BC describe a circle. From
the extremity C of the diameter draw any number of lines,
at any distance apart, passing through the circle and meeting
the line AB in 1' , 2' , 3', etc. Take the length from A to 9
and set it off from C on the same line to 9" '. Take the dis-
tance from 8' to 8 and set it off from C on the same line to
8", etc., for the other divisions, and through 9", 8", 7" , 6",
etc., draw the curve.

50 MECHANICAL DRAWING.

FiS.b' I2i To Draw Schiele's Anti-friction Curve.
— Let AB be the radius of the shaft and Bi, 2, 3, 4, etc., its
axis. Set off the radius AB on the straight edge of a piece
of stiff paper or thin celluloid and placing the point B on the
division 1 of the axis, draw through point A the line Ai.
Then lower the straight edge until the point B coincides with
2 and the points just touches the last line drawn, and draw
#2, and so proceed to find the points a, b, c, etc. Through
these points draw the curve.

Fig. 85.

Figb' %V. To Describe an Interior Epicycloid. —
Let the large circle X be the generator and the small circle
Y the director. Divide circle Y into any number of equal
parts, as B, H, /, /, etc. Draw radial lines and make HC,
ID, JE, KFy etc., each equal to the radius of the generator
X. With centers C, D, E, etc., describe arcs tangent at
H, I, J, etc. Make Hi equal to one of the divisions of the di-
rector as BH. Make I2 equal to two divisions, /3, three divi-
sions, etc., and draw the curve through the points 1, 2, 3, 4,

GEOMETRICAL DRAWING.

etc. This curve may also be described with a piece of cellu-
loid in a similar way to that explained for the cycloid.

It may not be out. of place here to describe a few of the

MOULDINGS USED IN ARCHITECTURAL WORK,

since they are often found applied to mechanical constructions.
Fi2b' so! To Describe the "Scotia." — 1, 1 is the top
line and 4, 4 the bottom line. From 1 drop a perpendicular
I, 4; divide this into three equal parts, as 1, 2, and 3.
Through the point 2 draw ab parallel to I, 1. With center 2
and radius 2, 1 describe the semicircle alb, and with center b
and radius ba describe the arc #5 tangent to 4, 4 at 5, draw
the fillets 1, 1 and 4, 4.

^ *

& Jh-

Fig. 86.

Fig. 87.

prob. 69. To Describe the "Cyma Recta."— Join 1,
3 and divide it into five equal parts, bisect 1, 2 and 2, 3, and
with radius equal to 1, 2 and 2, 3 respectively describe arcs
1, 2 and 2,3. Draw the fillets 1, 1 and 3, 3 and complete the
moulding.

Fig*' 88.' To Describe the "Cavetto" or "Hol-
low."— Divide the perpendicular 1, 2 into three equal parts
and make 2, 3 equal to two of these. From centers 1 and 3
with a radius somewhat greater than the half of 1, 3, describe
arcs intersecting at the center of the arc 1, 3,

MECHANICAL DRAWING.

Ffgb' sh'. To Describe the " Echinus," ''Quarter
Round," or "Ovolo." — Draw I, 2 perpendicular to 2, 3,
and divide it into three equal parts. Make 2, 3 equal to
two of these parts. From the points 2 and 3 with a radius
greater than half 1,3, describe arcs cutting in the center of
the required curve.

1 ' li. M

Fig 89.

Fi°b* 90 To Describe the " Apophygee.

Divide

3^ 4 into four equal parts and lay off five of these parts from
3 to 2. From points 2 and 4 as centers and radius equal to
2,3, describe arcs intersecting in the center of the curve.

Fig. 90.

Figb' 91! To Describe the "Cyma Reversa." — Make
4, 3 = 4, I. Join I, 3 and bisect it in the point 2. From the
points 1, 2 and 3 as centers and radii equal to about two-thirds
of 1 , 2 draw arcs intersecting at 5 and 6. Points 5 and 6
are the centers of the reverse curves.

Fi£b' It'. To Describe the " Torus."— Let 1, 2 be the
breadth. Drop the perpendicular 1, 2, and bisect it in the

GEOME TRICAL DRA WING.

point 3. With 3 as center and radius 3, I, describe the semi-
circle. Draw the fillets.

Fig. 92.

Fig. 93.

F%.b' 9§i An Arched Window Opening. — The curves
are all arcs of circles, drawn from the three points of the equi-
lateral triangle, as shown in the figure.

Firsb*94: To Describe the " Trefoil."— The equi-
lateral triangle is drawn first, and the angle 1,2,3 bisected by
the line 2, 4, which also cuts the perpendicnlar line 1, 6 in the
point 6. The center of the surrounding circles 1, 2 and 3 are
the centers of the trefoil curves.

Fir-b,95. To Describe the " Quatre Foil."— Draw
the square 1,2, 3, 4 in the position shown in the figure. The
center of the surrounding circles, point 5, is at the intersection
of the diagonals of the square. Points I, 2, 3, 4 of the square
are the centers of the small arcs.

Fig.b' 9e! To Describe the "Cinquefoil Orna-
ment." The curves of the cinquefoil are described from the
corners of a pentagon 1, 2, 3, 4, 5. Bisect 4, 5 in 6 and draw
2, 6, cutting the perpendicular in the point 7, the center of
the large circles.

Fi*gb' 97.' To Draw a Baluster. — Begin by drawing
the center line, and lay off the extreme perpendicular height,

MECHANICAL DRAWING.

the intermediate, perpendicular, and horizontal dimensions,
and finally the curves as shown in the figure.

Fig. 94.

Fig. 95.

Fig. 96.

Fig. 97.

DRAWING TO SCALE.

When we speak of a drawing as having been made to scale,
we mean that every part of it has been drawn proportionately
and accurately, either full size, reduced ox enlarged.

Very small and complicated details of machinery are usu-
ally drawn enlarged ; larger details and small machines may
be made full size, while larger machines and large details are
shown reduced.

When a drawing of a machine is made to a reduced or en-
larged scale the figures placed upon it should always give the
full-size dimensions, i.e., the sizes the machine should meas
ure when finished.

GEOMETRICAL DRAWING.

Figb' 98.' To Construct a Scale of Third Size or
4."= 1 FOOT. — Draw upon a piece of tough white drawing-
paper two parallel lines about \" apart and. about 14" long as
shown by a, Fig. 98. From A lay off distances equal to 4"
and divide the first space AB into 12 equal parts or inches by
Prob. 12. Divide AE'm the same way into as many parts as

it may be desired to subdivide the inch divisions on AB,
E

11W\8'7 (4\ 2 1

gcule I'* lfoot.

$' 5f

Fig. 98.

usually 8. When the divisions and subdivisions have been
carefully and lightly drawn in pencil, as shown by a, in Fig.
98, then the lines denoting jr"* i"> i", 1" ', and 3" should be
carefully inked and numbered as shown by (b). By a further
subdivision a scale of 2"= 1 foot may easily be made as shown
by (c) in Fig. 98.

CHAPTER III.
CONVENTIONS.

It is often unnecessary if not undesirable to represent cer-
tain things as they would actually appear in a drawing, espe-
cially when much time and labor is required to make them
orthographically true.

So for economic reasons draftsmen have agreed upon con-
ventional methods to represent many things that would other-
wise entail much extra labor and expense, and serve no par-
ticular purpose.

It is very necessary, however, that all draftsmen should
know how to draw these things correctly, for occasions will
often arise when such knowledge will be demanded ; and be-
sides it gives one a feeling of greater satisfaction when using
conventional methods to know that he could make them artis-
tically true if it was deemed necessary.

STANDARD CONVENTIONAL SECTION LINES.

Conventional section lines are placed on drawings to distin-
guish the different kinds of materials used when such drawings
are to be finished in pencil, or traced for blue printing, or to
be used for a reproduction of any kind.

Water-colors are nearly always used for finished drawings

and sometimes for tracings and pencil drawings.

The color tints can be applied in much less time than it

CONVENTIONS. 57

takes to hatch-line a drawing. So that the color method
should be used whenever possible.

FlG. 99. — This figure shows a collection of hatch-lined
sections that is now the almost universal practice among
draftsmen in this and other countries, and may be considered
standard.

No. 1. To the right is shown a section of a wall made of
rocks. When used without color, as in tracing for printing,
the rocks are simply shaded with India ink and a 175 Gillott
steel pen. For a colored drawing the ground work is made
of gamboge or burnt umber. To the left is the conventional
representation of water for tracings. For colored drawings
a blended wash of Prussian blue is added.

No. 2. Convention for Marble. — When colored, the
whole section is made thoroughly wet and each stone is then
streaked with Payne's gray.

No. 3. Convention for Chestnut. — When colored, a
ground wash of gamboge with a little crimson lake and burnt
umber is used. The colors for graining should be mixed in a
separate dish, burnt umber with a little Payne's gray and
crimson lake added in equal quantities and made dark enough
to form a sufficient contrast to the ground color.

No. 4. General Convention for Wood. — When colored the
ground work should be made with a light wash of burnt sienna.
The graining should be done with a writing-pen and a dark
/nixture of burnt sienna and a modicum of India ink.

No. 5. Convention for Black Walnut. — A mixture of
Payne's gray, burnt umber and crimson lake in equal quanti-
ties is used for the ground color. The same mixture is used
for graining when made dark by adding more burnt umber.

MECHANICAL DRAWING.

CON VEN TIOXS. 5 9

No. 6. Convention for Hard Pine. — For the ground
color make a light wash of crimson lake, burnt umber, and
gamboge, equal parts. For graining use a darker mixture of
of crimson lake and burnt umber.

No. 7. Convention for Building-stone. — The ground
color is a light wash of Payne's gray and the shade lines are
added mechanically with the drawing-pen or free-hand with
the writing-pen.

No. 8. Convention for Earth. — Ground color, India ink
and neutral tint. The irregular lines to be added with a writ-
ing-pen and India ink.

No. 9. Section Lining for Wrought or Malleable Iron. —
When the drawing is to be tinted, the color used is Prussian
blue.

No. 10. Cast Iron. — These section lines should be drawn
equidistant, not very far apart and narrower than the body
lines of the drawing. The tint is Payne's gray.

No. 1 1. Steel. — This section is used for all kinds of steel.
The lines should be of the same width as those used for cast-
iron and the spaces between the double and single lines should
be uniform. The color tint is Prussian blue with enough crim-
son lake added to make a warm purple.

No. 12. Brass. — This section is generally used for all
kinds of composition brass, such as gun-metal, yellow metal,
bronze metal, Muntz metal, etc. The width of the full lines.,
dash lines and spaces should all be uniform. The color tint
is a light wash of gamboge.

Nos. 13-20. — The section lines and color tints for these
numbers are so plainly given in the figure that further instruc-
tion would seem to be superfluous.

MECHANICAL DRAWING.

VISIBLE OBJECT LINES
Weight varied with discretion to suit
size of part.

INVISIBLE OBJECT LINES
Length of dash not less than \" nor
mo/i than tr", when possible space be-
tween dashes very short, not more than
3V'. dashes should be uniform in length
ani spaces uniform in width.

DIMENSION LINES
Continuous lines broken only to admit
the dimensions.

CENTER LINES
Long dashes, dots not more than 3V
long, space between dash and dot quite
short.

DIMENSION, PROJECTION LINES'
WITNESS LINES OR EXTEN-
SION LINES
First dash touching object tV" long,

short space, then dashes about \" long.

BREAK LINES
These lines to be drawn freehand with
the lettering pen.

ADJACENT PART LINES
Dashes \" long, dots not more than -h"
long, and space quite short.

ALTERNATE POSITION LINES
Use A when the limiting position is in-
dicated by a center line only, dashes f"
and dots \" long, very close together.
Use B when the alternate position is
shown by the base outlines of the object.
Dash £•", dot £", very close together.

CUTTING PLANE LINES
A dashes about f" long and all the
same length, dots ■&" long, close together.
Use B when it is not convenient to draw
the line through the view.

Heavy
h"

BORDER LINES; REFERENCE
ARROW LINES

Should always be drawn straight with
ruling pen and set obliquely, i.e., neither
vertically nor horizontally.

Fig. 100.
CONVENTIONAL LINES.
Fig. 100. — There are four kinds:

(1) The Hidden Line. — This line should be made of short
dashes of uniform length and width, both depending some-
whta on the size of the drawing. The width should always

CONVENTIONS. 6l

be slightly less than the body lines of the drawing, and the
length of the dash should never exceed £'\ The spaces
between the dashes should all be uniform, quite small, never
exceeding T\". This line is always inked in with black ink.

(2) The Line of Motion. — This line is used to indicate
point paths. The dashes should be made shorter than those of
the hidden line, just a trifle longer than dots. The spaces
should of course be short and uniform.

(3) Center Lines. — Most drawings of machines and parts
of machines are symmetrical about their center lines. When
penciling a drawing these lines may be drawn continuous and
as fine as possible, but on drawings for reproductions the black-
inked line should be a long narrow dash and two short ones
alternately. When colored inks are used the center line should
be made a continuous red line and as fine as it is possible to
make it.

(4) Dimension Lines and Line of Section. — These lines
are made in black with a fine long dash and one short dash
alternately. In color they should be continuous blue lines.
Colored lines should be used wherever feasible, because they
are so quickly drawn and when made fine they give the drawing
a much neater appearance than when the conventional black
lines are used. Colored lines should never be broken.

CONVENTIONAL BREAKS.

FlG. 10 1. — Breaks are used in drawings sometimes to indi-
cate that the thing is actually longer than it is drawn, some-
times to show the shape of the cross-section and the kind of
material. Those given in Fig. 10 1 show the usual practice.

MECHANICAL DRAWING.

CROSS-SECTIONS.
FIG. 102. — When a cross-section of a pulley, gear-wheel
or other similar object is required and the cutting-plane passes

MMAWAmm^ «a mi mmmmvmvw;

■M.WM.VWAVVVVVVVV\VV^VVvkV^W'0

Fig. ioi.

Fig. 102.
through one of the spokes or arms, then only the rim and hub
should be sectioned, as shown at xx No. I and z No. 2, and
the arm or spoke simply outlined. Cross-sections of the arms
may be made as shown at AA No. 2. In working drawings of
gear-wheels only the number of teeth included in one quadrant
need be drawn; the balance is usually shown by conventional
lines, e.g., the pitch line the same as a center line, viz., a long dash
and two very short ones alternately or a fine continuous red line.
The addendum line (d) and the root or bottom line (b) the
same as a dimension line, viz., one long dash and one short

CONVENTIONS.

dash alternately or a fine continuous blue line. The end ele-
vation of the gear-teeth should be made by projecting only
the points of the teeth, as shown at No. 2.

CONVENTIONAL METHODS OF SHOWING SCREW-THREADS
IN WORKING DRAWINGS.

FlG. 103. — No. I, shows the convention for a double
V thread, U. S. standard; No. 2, a single V thread; No. 3,
a single square thread; No. 4, a single left-hand V thread;
No. 5, a double right hand square thread; No. 6, any
thread of small diameter; No. 7, any thread of very small
diameter. The true methods for constructing these threads
are explained on pages 99-101, Figs. 137— 139.

In No. 6. the short wide line is equal to the diameter
of the thread at the bottom. The distance between the
longer narrow lines is equal to the pitch, and the inclination
is equal to half the pitch.

The short dash lines in No. 7 should be made to corre-

it ntj

Fig. 103.

spond to the diameter of the thread at the bottom. After
some practice these lines can be drawn accurately enough by
the eye.

CHAPTER IV.
LETTERING AND FIGURING.

THIS subject has not been given the importance it deserves
in connection with mechanical drawing. Many otherwise ex-
cellent drawings and designs as far as their general appearance
is concerned have been spoiled by poor lettering and figuring.

All lettering on mechanical drawings should be plain and
legible, but the letters in a title or the figures on a drawing
should never be so large as to make them appear more prom-
inent than the drawing itself.

The best form of letter for practical use is that which gives
the neatest appearance with a maximum of legibility and re-
quires the least amount of time and labor in its construction.

This would naturally suggest a " free-hand " letter, but be-
fore a letter can be constructed " free-hand " with any degree
of efficiency, it will be necessary to spend considerable time
in acquiring a knowledge of the form and proportions of the
particular letter selected.

It is very desirable then that after the stud.ent has care-
fully constructed as many of the following plates of letters and
numbers as time will permit and has acquired a sufficient
knowledge of the form and proportions of at least the " Ro-
man " and " Gothic " letters; he should then adopt some one

LETTERING AND FIGURING. 65

style and practice that at every opportunity, until he has at-
tained some proficiency in its free-hand construction.

When practicing the making of letters and numbers free-
hand, they should be made quite large at first so as to train
the hand.

The " Roman " is the most legible letter and has the best
appearance, but is also the most difficult to make well, either
free-hand or mechanically. However, the methods given for
its mechanical construction, Figs. 104 and 105, will materially
modify the objections to its adoption for lettering mechanical
drawings.

The " Gothic" letter is a favorite with mechanical drafts-
men, because it is plain and neat and comparatively easy to
construct. (See Fig. 106.)

Among the type specimens given in the following pages
the Bold-face Roman Italic on page 70 is one of the best
for a good, plain, clear, free-hand letter, and is often used
with good success on working drawings. Gillott's No. 303
steel pen is the best to use when making this letter free-hand.

The "Yonkers" is a style of letter that is sometimes
used for mechanical drawings. It is easy to construct with
either F. Soennecken's Round Writing-pens, single point, or
the Automatic Shading-pen. But it lacks legibility, and is
therefore not a universal favorite.

A good style for " Notes" on a drawing is the ''Gothic
Condensed " shown on page 70.

Wrhen making notes on a drawing with this letter, the
only guides necessary are two parallel lines, drawn lightly in
pencil. The letters should be sketched lightly in pencil first,

MECHANICAL DRAWIXG.

and then carefully inked, improving spacing and proportions
to satisfy the practiced eye.

FIGURING.

Great care should be taken in figuring or dimensioning a
mechanical drawing, and especially a working drawing.

To have a drawing accurately, legibly, and neatly figured
is considered by practical men to be the most important part
of a working drawing.

There should be absolutely no doubt whatever about the
character of a number representing a dimension on a drawing.

Many mistakes have been made, incurring loss in time,
labor, and money through a wrong reading of a dimension.

Drawings should be so fully dimensioned that there will
be no need for the pattern-maker or machinist to measure any
part of them. Indeed, means are taken to prevent him from
doing so, because of the liability of the workman to make
mistakes, so drawings are often made to scales which are dif-
ficult to measure with a common rule, such as 2" and 4" =
1 ft.

The following books, among the best of their kind, are
recommended to all who desire to pursue further the study
of " Lettering" : Plain Lettering, by Prof. Henry S. Jacoby,
Cornell University, Ithaca, N. Y. ; Lettering, by Charles W.
Reinhardt, Chief Draftsman, Engineering News, New York ;
Free-hand Lettering, by F. T. Daniels, instructor in C. E. in
Tufts College.

LETTERING AND FIGURING.

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MECHANICAL DRAWING.

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LETTERING AND FIGURING.

70 MECHANICAL DRAWING.

18-Point Roman.

ABCDEFGHIJKLMNOPQKSTUVWX
YZ abcdefghijklmnopqrstuvwxyz
1234567890

[8-Point Italic.

ABCDEFGHIJKLMNOPQRSTUV

WX YZ abcdefghijklmnopqrs tuvwxyz

i?.- Point Cushing Italic.

ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklm
nopqrstuvwxyz 123456 7890

28-Point Boldface Italic.

ABCDEFGHIJKLM
NOPQRSTUVWXYZ

abcdefghijklmnopqrstu
vwxyz 12S4S67890

Two-Line Nonpareil Gothic Condensed.

ABCDEFGHIJKLMNOPQRSTUVWXYZ 1234567890

Three-Line Nonpareil Lightface Celtic.

ABCDEFGHIJKLMNOPQR

STUVWXYZ abedefghijkl
mnopqrstu vwxyz
1234567890 "

LETTERING AND FIGURING. *]\

18-Point Chelsea Circular.

ABCDEFGHIJKLMNOPQRSTUVWX

YZ abcdefgh(ijl\lmT^opqrstuvwxyz

1234567890

x8-Point Elandkay.

ABCDEFGHIJKLnNOFQRSTUVVXYZ
1234567890

18-Point Quaint Open.

WITZ 1 234 J67SS©

28-Point Roman.

ABCDEFGHIJKLM
NOPQRSTUVWXYZ

abcdefghij klmnopqrstu
vwxyz 1234567890

28-Point Old-Style Italic.

ABCDEFGHIJKLMNOP

QRSTUVM/XYZ abcdefg
h ijklm n opqrstuvwxyz
12345678QO

72 MECHANICAL DRAWING.

12-Point Victoria Italic.

ABCDEFCHIJKLMNOPQRSTU
YWXYZ 1234567890

18-Point DeVinne Italic.

ABCDEFGHIJKLMNOPQRSTV

VWXYZ abcdefghijklmnopqrst

uvwxyz 1234567890

22-Point Gothic Italic.

ABCDEFGHIJKLMNOPQRSTUVWXYZ

abcdefghijklmnopqrstuuwxyz

1234567890

Double- Pica Program.

ABCDEFGHIJKLMNO

PQRSTUYWXYZ

abcdefghijklmnopqrstuv

wxyz 1234567890

Nonpareil Telescopic Gothic.

ABCDEFGHIJKLMNOPQRSTUVWXYZ 1234567S90

LETTERING AND FIGURING. 73

24-Point Gallican.

ABCDEFGHIJKL
MNOPQRSTUVW
XYZ 1234567890

Two-Line Virile Open.

JBCPETQHUHi\M0PQR5TH»WXYZ

4WefgWJHiw©p^jrst(ia^¥xp
3456F8

, AG]

(0)

22-Point Old-Style Roman.

ABCDEFGHIJKLMNOPQRST

UVWXYZ abcdefghijklmnopqrst

uvwxyz 1234567890

36-Point Yonkers.

y^ ctbcMgfyijklmnopqr
stutwxya 1(23^567890

CHAPTER V.
ORTHOGRAPHIC PROJECTION.

Orthographic Projection, sometimes called Descrip-
tive Geometry and sometimes simply Projection, is one of
the divisions of descriptive geometry; the other divisions are
Spherical Projection, Isometric Projection, Shades and
Shadows, and Linear Perspective.

In this course we will take up only a sufficient number of
the essential principles of Orthographic Projection, Isometric
Projection, and Shades and Shade Lines, to enable the stu-
dent to make a correct mechanical drawing of a machine or
other object.

Orthographic Projection is the science and the art of rep-
resenting objects on different planes at right angles to each
other, by projecting lines from the point of sight through the
principal points of the object perpendicular to the Planes of
Projection,

There are commonly three planes of projection used, viz.,
the H. P. or Horizontal Planey the V. P. or Vertical Plane,
and the Pf P. or Profile Plane.

These planes, as will be seen by Figs. 107 and 109, inter-
sect each other in a line called the /. L. or Intersecting Line,
and form four angles, known as the first, second, third, and

OR THO GRA PHIC PR OJE C TION,

fourth Dihedral Angles. Figs. 107 and 109 are perspective
views of these angles.

An object may be situated in any one of the dihedral
angles, and its projections drawn on the corresponding co-
ordinate planes.

Problems in Descriptive Geometry are usually worked out
in the first angle, and nearly all English draftsmen project
their drawings in that angle, but in the United States the
third angle is used almost exclusively. There is good reason
for doing so, as will be shown hereafter.

We will consider first a few projection problems in the

first angle, after which the third angle will be used throughout.

Fig. 107.

H.P., Fig. 107, is the Horizontal Plane, V.P. the Vertical
Plane, and I.L. the Intersecting Line.

The Horizontal Projection of a point is where a perpen-
dicular line drawn through the point pierces the H.P.

The Vertical Projection of a point is where a per. line
drawn through the point pierces the V.P.

Conceive the point a, Fig. 107, to be situated in space 4"
above the H.P. and 3" in front of the V.P. If a line is
passed through the point a per. to H.P. and produced until

76 MECHANICAL DRAWING.

it pierces the H.P. in the point ah, ah will be the Hor. Proj.
of the point a.

If another line is projected through the points per. to the
V.P. until it pierces the V.P. in the point av, av is the ver-
tical projection of the point a.

If now the V.P. is revolved upon its axis I.L. in the di-
rection of the arrow until it coincides with the H.P. and let
the H.P. be conceived to coincide with the plane of the
drawing-paper, the projections of the point a will appear as
shown by Fig. 108.

The vertical projection av 4" above the I.L. and the
horizontal projection ah 3" below the I.L. both in the same
straight line.

In mechanical drawing the vertical projection cC is called
the Elevation and the horizontal projection ah the Plan.

The projections of a line are found in a similar manner,
by first finding the projections of the two ends of the line,
and joining them with a straight line.

Let ab be a line in space i\" long, parallel to the V.P.
and perpendicular to the H.P. One end is resting on the
H.P. 2i" from the V.P.

The points a and b will be vertically projected in the
points av and bv. Join avbv. avbv is the vertical projection of
the line ab.

When a line is perpendicular to one of the planes of pro-
jection, its projection on that plane is a point, and the projec-
tion on the other plane is a line equal to the line itself.

ab, Fig. 107, is perpendicular to the H.P., therefore its
proj. on the H.P. when viewed in the direction ab will be
seen to be a point.

ORTHOGRAPHIC PROJECTION.

Conceive now the V.P. revolved as before, the V. proj.
will be found to be at avbv, Fig. 108, and the H. proj. at the
point ah.

cd, Fig. 107, is a line parallel to the H.P. and perpendic-
ular to the V.P. Its elevation or V. proj. is the point dv, Fig.
108, and its plan or H. proj. the line (^dh perpendicular to
the Intersecting Line and equal in size to the line itself.

Planes or Plane Surfaces bounded by lines are projected
by the same principles used to project lines and points.

Let aavbvb, Fig. 107, be a plane at right angles to and
touching both planes of projection.

The elevation of the front upper corner a is projected in
the point av. The elevation of the front lower corner b is pro-
jected in the point b° , Join avbv. avbv is the vertical projection
of the front edge ab of the plane. The plan of the front

*
b

Fig. 108.

upper corner is projected in the point b and the point av in the
point bv. A straight line joining bbv is the plan or horizontal
projection of the top edge of the plane.

On the drawing-paper the plan and elevation of the plane
acfb a would be shown as a continuous straight line a0 to ah
Fig. 108.

MECHANICAL DRAWING

Solids bounded by plane surfaces are projected by means
of the same principles used to project planes, lines, and points.

C, Fig. 107, is a cube bounded by six equal sides or sur-
faces. The top and bottom being parallel to the H.P. and
the front and back parallel to the V.P., the vert. proj. is a
square above I.L. equal in area to any one of the six faces
of the cube. The hor. proj. is a similar square belowT.L.

These projections are shown at C, Fig. 108, as they would
appear on the drawing-paper.

The foregoing illustrates a few of the simple principles of
projection in relation to points, lines, and solids when placed
in the first dihedral angle, and we find that the plan is always
below and the elevation always above the I.L.

Let us now consider the same problems when situated in
the third angle. The point a, Fig. 109, is behind the V.P.

Fig. 109.

and below the H.P. Draw through a perpendiculars to the
plane of projection. The Hor. proj. is found at ah and the
vert. proj. at av.

Conceive again the V.P. to be revolved in the direction
of the arrow until it coincides with the H. P. The hor. proj.

ORTHOGRAPHIC PROJECTION.

will then appear at ah above the I.L. and the vert. proj. at av
below the I.L., Fig. no. And so with the lines, the planes,
and the solids.

1 1

-b '

Fig. iio.

In order to still further explain the use of the planes of
projection, with regard to objects placed in the third angle,
let us suppose a truncated pyramid surrounded by imaginary
planes at right angles to each other, as shown by Fig. ill.

Fig. hi.

With a little attention it will easily be discerned that the
pyramid is situated in the third dihedral angle, and that in
addition to the V. and H. planes, we have passed two profile
planes at right angles to the V. and H. planes, one at the right-
hand and one at the left.

When the pyramid is viewed orthographically through
each of the surrounding planes, four separate views are had,

MECHANICAL DRAWING.

exactly as shown by the projections on the opposite planes,
viz., a Front View, Elevation, or Vert. Proj. at F. ; a Right-
hand View, Right-end Elevation, or Right-profile Projection
at R. ; a Left-hand View, Left-end Elevation, or Left-profile
Projection at L. ; a Top View, Plan or H. Proj. at P.

If we now consider the V.P. and the right and left profile
planes to be revolved toward the beholder until they coincide,
using the front intersecting lines as axes, the projections of the
pyramid will be seen as shown by Fig. 1 12, which when the

Fig. 112.

imaginary planes and projecting lines have been removed, will
be a True Drawing or Orthographic Projection of the truncated
pyramid.

NOTATION.

In the drawings illustrating the following problems and
their solutions the given and required lines are shown wide and
black. Hidden lines are shown broken into short dashes a little
narrower than the visible lines. Construction or projection lines
are drawn with very narrow full or conti?iuous black lines.

ORTHOGRAPHIC PROJECTION. 8 I

When convenient very narrow, continuous blue lines are some-
times used.

The Horizontal Plane is known as the H.P., the Vertical
Plane as V.P. and the Profile Plane as Pf.P.

A point in space is designated by a small letter or figure,
its projection by the same letter or figure with small h or v
written above for the horizontal or vertical projection respec-
tively.

In some compjicated problems where points are designated
by figures their projections are named by the same figures
accented.

Drawings should be carefully made to the dimensions
given, the scale to be determined by the instructor.

The student should continually endeavor to improve in
inking straight lines, curves, and joints.

In solving the following problems the student should have
a model of the co-ordinate planes for his own use. This can
be made by taking two pieces of stiff cardboard and cutting a
slot in the center of one of them large enongh to pass the
folded half of the other through it ; when unfolding this half a
model will be had like that shown by Fig. 107 or 109.

All projections shall now be made from the third,
dihedral angle.

PROB. 1. — A point a is situated in the third dihedral
angle, \" below the H.P. and 3" behind the V.P.

It is required to draw its vertical and horizontal projec-
tions.

Draw a straight line ahav, Fig. 113, perpendicular to I.L.
and measure off the point a° \" below I.L. and the point ah
3" above I.L.

MECHANICAL DRAWING.

a" is the vertical and ah the horizontal projection in the
same straight line d°ah.

The student should demonstrate this with his model.

PROB. 2. — Draw two projections of a line 3" long parallel
to both planes, |" below the H.P. and 2" behind the V.P.

As the line is parallel to both planes, both projections will
be parallel to the I.L.

Draw d"bv the vert. proj. of the line 3" long, Fig. 1 14, par-
allel to I.L. and f" below it. Draw the hor. proj. 2" above
the I.L. and parallel to it, making it the same length as the

Fig. 113. Fig. 114. Fig. 115. Fig. 116. Fig. 117.

vert. proj. by drawing lines perpendicular to I.L. from the
points a" and b° to ah and bh.

Prob. 3. — To draw the hor. and vert, projs. of a straight
line 3" long, per. to the vert, plane, Fig. 115.

As the line is per. to the vert, plane the vert. proj. will be
a point below the I.L. and the hor. proj. will be parallel to
the horizontal plane and per. to I.L.

PROB. 4. — To draw the plan and elevation of a straight
line 6" long making an angle of 45 ° with the vert, plane and
and par. to the hor. plane, Fig. 116.

ORTHOGRAPHIC PROJECTION. 83

The plan or hor. proj. will be above the I.L. and make an
angle of 450 with it. The elevation or vert. proj. will be
below and par. to I.L.

Draw from the point ah at any convenient distance from
I.L. a straight line ahbh 6" long, making an angle 45 ° with I.L.

Draw avbv par. to I.L. at a convenient distance below it.
The length of the elevation or vert. proj. is determined by
dropping perpendiculars from the end of the hor. proj. ahbh to
the points a"b\

PROB. 5, FlG. 117. — To find the true length of a straight
line oblique to both planes of projection and the angle it
makes with these planes.

avbv and ahbh are the projections of a straight line oblique
to V.P. and H.P. Using a" as a pivot, revolve the line avbv
until it becomes parallel to I.L. as shown by avblv. From the
point b? erect a per. Through the point bh draw a line par. to
I.L. cutting the per. in the point bxk.

The broken line ahbxh is the true length of the line ab,
and the angle 0 is the true angle which the line makes with
V.P.

To find the angle it makes with H.P. :

Using bh as a pivot, revolve the line bhah until it becomes
par. to I.L. as shown by bhaf. From the point axh drop a per.
Through the point a" draw a line par. to I.L. intersecting the
per. at the point a?o is the angle which the line ab makes
with H.P. and the broken line a?bv is again its true length.

PROB. 6, FlG. 118. — To project a plane surface of given
size, situated in the third angle and par. to the V.P.

Let abed be the plane surface 3" long X 2" wide. If
we conceive lines to be projected from the four corners of the

84 MECHANICAL DRAWING.

plane surface to the V.P. and join them with straight lines we
will have its V. projection avbvevdv and shown by Fig. 1 1 8.
And as the plane surface is par. to the V.P. it must be per
to the H.P. since the planes of projection are at right angles
to each other. So the plan or H. projection will be a straight
line equal in length to one of the sides of the plane surface.

At a convenient distance above I.L. draw a straight line,
and from the points a°bv project lines at right angles to I.L.,
cutting the straight line in the points ahb.k The line ahbh is
the hor. proj. of the plane surface abed.

PROB. 7, FlG. ii8. — To draw the projections of a plane
surface of given dimensions when situated in the third angle
perpendicular to the H.P. and making an angle with the V.P.

Let the plane surface be 3" X 2" as before and let the
angle it makes with V.P. be 6o°.

To draw the plan :

At a convenient distance above I.L. and making an angle
of 6o° with it, draw ahb1h, Fig. 1 18, 2" long. From b,h drop a
per. cutting a°bv in the point b" and c°dv in the point dxv, then
the rectangle avb1vdlvev will be the vert. proj. or elevation of
the plane surface abed.

Prob. 8, Fig. 119. — To draw the projections of the same
plane surface (1) when parallel to the H.P., (2) when making
an angle of 300 with H.P. and per. to V.P., (3) when mak-
ing an angle of 6o° with H.P. and per. to V.P., and (4) when
per. to both planes.

Fig. 119 shows the projections; further explanations are
unnecessary.

PROB. 9, Figs. 1 19 AND 120. — To draw the projections of

ORTHOGRAPHIC PROJECTION

the same plane surface when making compound angles with
the planes of projection.

Let the plane make an angle of 300 with H.P., as in the
second position of Prob. 8, Fig. 119, and in addition to that,
revolve it through at angle of 300. First, draw the plane
parallel to H.P., as shown by ahchbhdh, Fig. 119, the true size
of the plane.

Fig. 119. Fig. 120.

Its elevation will be the straight line avbv parallel to I.L.
Next revolve avbv, using av as a pivot, through an angle of
300, to the position avb? , which is its vert. proj. when making
an angle of 300 with H.P. Its plan is projected in cfb^d*.

Now as the plane is still to make an angle of 300 with
H.P. after it has been revolved through an angle of 300 with
relation to the V.P., its hor. proj. will remain unchanged.

With a piece of celluloid or tracing-paper trace the hor.
proj. cfb^df, lettering the points as shown, and revolve the

86 MECHANICAL DRAWING.

tracing through the angle of 300, or, which is the same thing,
place the tracing so that the line ahch will make an angle of
6o° with I.L., and with a sharp conical-pointed pencil trans-
fer the four points to the drawing-paper and join them by
straight lines, as shown by Fig. 120.

And as the line <zVl retains its position relative to H.P.
after the revolution, its elevation will be found at avcv, Fig.
120, in a straight line drawn through avbv, Fig. 119, intersect-
ing perpendiculars from #V, Fig. 120. And the vert. proj.
of the points bfdf will be found at h"d™, Fig. 120, in a straight
line drawn through b*, Fig. 1 19, parallel to I.L. and intersect-
ing pers. from b*df> join with straight lines the points

Draw the projections of the plane when making an angle
of 6o° with H.P. and revolved through an angle of 300 with
relation to V.P.

Draw the projections of the plane when making an angle
of 6o° with the V.P. and per. to the H.P., Fig. 120.

PROB. 10. — To draw the projections of a plane surface of
hexagonal form in the following positions: (1) When one
of its diagonals is par. to the V.P. and making an angle of
450 with the H.P. (2) When still making an angle of 450
with the H.P. the same diagonal has been revolved through
an angle of 6o°.

Draw the hexagon ih2h3h4h$h6ht Fig. 121, at any con-
venient distance above I.L., making the inscribed circle
= 2%" . This will be its hor. proj. and 2va?&\v its vert, proj.,
the diagonal \h2h being par. to both planes of proj. With
V as an axis revolve 6V4V2V through an angle of 45 °. Through
the points 2^4/6/ erect pers. to the points 61*5,*41*31* and 2*

ORTHOGRAPHIC PROJECTION.

and join them with straight lines. These are the projs. in
the first position. Now trace the hor. proj, 1*, 2/', etc., on
a piece of celluloid or tracing-paper and revolve the tracing
until the diagonal 1*2,* makes an angle of 6o° with the I.L.,
Fig. 122. Next draw pers. from the 6 points of the hexag-
onal plane to intersect hors. from the corresponding points of
the elevation in Fig. 121, join the points of intersection with

straight lines, and so complete the projections of the second
position, Fig. 122.

PROB. 11, FIGS. 123 AND 124. — Draw the projs. of a cir-
cular plane (1) when its surface is par. to the vert, plane, (2)
when it makes an angle of 45 ° with the V.P., and (3) when
still making an angle of 450 with the V.P. it has been re-
volved through an angle of 6o°.

First position: Draw the circular plane iv, 2V, y, 4", etc.,
Fig. 123, below the I.L. with a radius = 1}" and divide and
figure it as shown.

MECHANICAL DRAWING:

Since the plane is par. to V.P. its hor. proj. will be a
straight line i\ 2h, etc.

For the second position revolve the said hor. proj. through
the required angle of 450 to the position ah . . . . 1^, Fig. 123,
and through each division in ik . . . . ah draw arcs cutting
ah . . . . ih in points 2h$h . . . This is the hor. proj. of the
plane when making an angle of 45 ° with the V.P.

The elevation is found by dropping pers. from the points
in the hor. proj. ah . . .1/ to intersect hor. lines drawn
through the correspondingly numbered points in the eleva-

Fig. 123.

Fig. 124.

tion and through these intersections draw the elevation or
vert. proj. of the second position.

For the third position make a tracing of the elevation of
the second position, numbering all the points as before, and
place the tracing so that the diameter yvf° makes the required
angle of 6o° with the I.L. and transfer to the drawing-paper.

ORTHOGRAPHIC PROJECTION. 89

The result will be the elevation of the third position shown
below the I.L., Fig. 124. Its hor. proj. is found by drawing
pers. through the points 1, 2, 3,4 ... to intersect hors. drawn
through the corresponding points in the hor. proj. of the 2d
position and through these intersections draw the plan or hor.
proj. of the third position, Fig. 124.

PROB. 12, FlG. 125. — Draw the projs. of a regular hexag-
onal prism, 3" high and having an inscribed circle of 4%"
diam. : (1) When its axis is par. to the V.P. (2) Draw the
true form of a section of the prism when cut by a plane
passing through it at an angle of 300 with its base. (3)
Draw the projection of a section when cut by a plane passing
through XX, Fig. 125, per. to both planes of proj.

The drawing of the I.L. may now be omitted.

For the plan of the first part of this prob. draw a circle'
with a radius = to 2T5¥", and circumscribe a hexagon about it,
as shown by ah, bh, bh, etc., Fig. 125. To project the elevation,
draw at a convenient distance from the plan a hor. line par.
to ahd!\ and 3" below it another line par. to it. From the
points ahbh^dh, drop pers. cutting these par. lines in the points
avbvcvdv , thus completing the elevation of the prism.

Second condition : Draw the edge view or trace of the
cutting plane iV> making an angle of 300 with the base of the
prism, locating the lower end 4' one-half inch above the base;
parallel to i'4', and at a convenient distance from it draw a
straight line 1,4; at a distance of 2<f$n on each side of 1,4
draw lines 3, 2 and 5, 6 parallel to 1,4, and through the
points r'2'3'4' let fall pers. cutting these three par. lines in
the points 1, 2, 3, 4, 5, 6; join these points by straight lines

9°

MECHANICAL DRAWING.

as shown, and a true drawing of the section of the prism as
required will result.

For the third condition of the problem :

Let XX be the edge view of the cutting plane and con
ceive that part of the prism to the right of XX to be removed

b c

From the hor. proj. of the prism draw a right-hand elevation
or profile proj., and through the points XX draw the lines en-
closing the section, and hatch-line it as shown.

Prob. 13.— To draw the development of the lower part
of the prism in the elevation of the last problem.

ORTHOGRAPHIC PROJECTION. 9 1

To the right of the elevation in Fig. 125, prolong the base
line indefinitely and lay off upon it the distances ab, be, cd,
etc., Fig. 126, each equal in length to a side of the hex. At
these points erect pers., and through the points 1*2' $'4! draw
hor. lines intersecting the pers. in 4, 3, 2, 1, etc. At be
draw the hex. ahbhbk ^c* ^d* of the last prob. for the base, and
at 1, 2 draw the section 1, 2, 3, 4, 5, 6 for the top.

PrOB. 14, FIG. 127. — To draw the projs. of a right cylin-
der 3" diam. and 3'' long. (1) When its axis is per. to the
H.P. (2) Draw the true form of a section of the cylinder,
when cut by a plane per. to the V.P. making an angle of 300
with the H.P. (3) Draw a development of the upper part of
the cyl.

For the plan of the first condition, describe the circle 1' ' ,
2' \ etc., with a radius = ij" and from it project the eleva-
tion, which will be a square of 3" sides.

For the second condition: Let 1, 7 be the trace of the
cutting plane, making the point 7, \" from the top of the cyl.
Divide the circle into 12 equal parts and let fall pers. through
these divisions to the line of section, cutting it in the points
1, 2, 3,4, etc. Parallel to the line of section 1, 7 draw \"j"
at a convenient distance from it, and through the points
1, 2, 3, 4, etc., draw pers. to 1,7, intersecting and extending
beyond \"j". Lay off on these pers. the distances 6 8" —
6'8', and 5"c/' = 5 '9 ', etc., and through the points 2", 3",
4", etc., describe the ellipse.

For the development: In line with the top of the eleva-
tion draw the line g'g" equal in length to the circumference of
the circle, and divide it into 12 equal parts a', b' , etc., a', b" ,
etc. Through these points drop pers. and through the points

MECHANICAL DRAWING.

I, 2, 3, etc., draw hors. intersecting the pers. in the points
I, 2, 3, etc., and through these points draw a curve.

Tangent to any point on the straight line draw a 3" circle
for the top of the cyl. and tangent to any suitable point on
the curve transfer a tracing of the ellipse.

PROB. 15, FlG. 128. — Draw the projections of a right cone
7" high, with a base 6" in diam., pierced by aright cyl. 2" in

Fig. 127.

diam. and 5" long their axes intersecting at right angles 3"
above the base of the cone and par. to V.P. Draw first the
plan of the cone with a radius = 3".

At a convenient distance below the plan draw the elevation
to the dimensions required.

3" above the base of the cone draw the center line of the
cyl. CD, and about it construct the elevation of the cyl., which
will appear as a rectangle 2" wide and 2%" each side of the
axis of the cone. The half only appears in the figure.

OR THO G RA PHIC PR OJE C TION.

To project the curves of intersection between the cyl. and
cone in the plan and elevation : Draw to the right of the cyl.
on the same center line a semicircle with a radius equal that
of the cyl. Divide the semicircle into any number of parts,

Fig. 128.

Fig. 129.

as I, 2, 3, 4, etc. Through 1, 1 draw the per. A" 1" equal
in length to the height of the cone, and through A" draw the
line A" 4" tangent to the semicircle at the point 4, and through
the other divisions of the semicircle draw lines from A" to the
line i'V'> meeting it in the points $"2r,\

From all points on the line i'V, viz-. i'VW'* erect

94 MECHANICAL DRAWING.

pers. to the center line of the plan, cutting it in the points
ii//2i"3i"4i"> anc* with i" as the center draw the arcs 2/ -2,
3,"-3, 4//-4 above the center line of the plan, and through the
points 2, 3, 4 draw hors. to intersect the circle of the plan in
the points 2/3V> and lay off the same distances on the other
side of the center line of the plan in same order, viz., 2/3/4/.
Through each of these points on the circumference of the circle
of the plan draw radii to its center A', and through the same
points also in the plan let fall pers. to the base of the elevation
of the cone, cutting it in the points 2/3/4' ; and from the apex
A of the elevation of the cone draw lines to the points 2/34' on
the base. Hor. lines drawn through the points of division 2,
3, 4 on the semicircle will intersect the elements A— 2', A— 3',
A-4' of the cone in the points 2' 3' ^ \ these will be points in
the elevation of the curve of intersection between the cylinder
and the cone.

The plan of the curve is found by erecting pers. through
the points in the elevation of the curve to intersect the radial
lines of the plan in correspondingly figured points, through
which trace the curve as shown. Repeat for the other half
of the curve.

Prob. 16, FlG. 129. — To draw the development of the
half cone, showing the hole penetrated by the cyl.

With center 4/', Fig. 129, and element A\' of the cone,
Fig. 128, as radius, describe an arc equal in length to the semi-
circle of the base of the cone. Bisect it in the line 4/' 1, and
on each side of the point 1 lay off the distances 2, 3, 4, equal
to the divisions of the arc in the plan Fig. 128, and from these
points draw lines to 4", the center of the arc. Then with
radii A-a> b, c, d, e, respectively, on the elevation Fig. 128,

OR THO G RA PHI C PR OJE CTION.

and center 4," draw arcs intersecting the lines drawn from the
arc XX to its center 4/'. Through the points of intersection
draw the curve as shown by Fig. 129.

PROB. 17, FlG. 130. — To draw the development of the
half of a truncated cone, given the plan and elevation of
the cone.

Fig. 130.

Divide the semicircle of the plan into any number of parts,
then with A as center and A 1 as radius, draw an arc and lay
off upon it from the point 1 the divisions of the semicircle
from 1 to 9, draw gA. Then with center A and radius AB
draw the arc BC. iBCg is the development of the half of
the cone approximately.

90 MECHANICAL DRAWING.

PROB. i8,*Fig. 131. — To draw the curve of intersection of
a small cyl. with a larger. To the left of the center-line of
Fig. 131 is a half cross-section, and to the right a half eleva-
tion of the two cyls.

Draw the half plan of the small cyl., which will be a
semicircle, and divide it into any convenient number of parts,
say 12.

From each of these divisions drop pers.

On the half cross-section these pers. intersect the circum-
ference of the large cyl. in the points i', 2', etc. Through

Fig. 132.

these points draw hors. to intersect in corresponding points
the pers. on the half elevation. Through the latter points
draw the curve of intersection C.

Prob. 19. — To draw the development of the smaller cyl.
of the last prob.

Draw a rectangle, Fig. 132, with sides equal to the circum-

ORTHOGRAPHIC PROJECTION. 97

ference and length of the cyl. respectively, and divide it into
24 equal parts.

Make AB, 1 i', 3 3', etc., Fig. 132, equal to AB, 1/1",
2' 2", 3/3//, etc., Fig. 131, and draw the developed curve of
intersection.

PROB. 20. — To draw the orthographic projections of a
cylindrical dome riveted to a cylindrical boiler of given
dimensions.

Let the dimensions of the dome and boiler be : dome
26\" diam. X 27" nigh, boiler 54" diam., plates J" thick.

Apply to the solution of this problem the principles ex-
plained in Prob. No. 18, Fig. 131.

When your drawings are completed, compare them with
Figs. 133 and 134, which are the projections required in the
problem.

Letter or number the drawing and be prepared to explain
how the different projections were found.

Prob. 21. — To draw the development of the top gusset-
sheets of a locomotive wagon-top boiler of given dimensions.

First draw the longitudinal cross-section of the boiler to
the dimensions given by Fig. 135, using the scale of 1" =
1 ft.

Then at any convenient . point on your paper draw a
straight line, and upon it lay off a distance AB 35-2" long =
the straight part of the top of the gusset-sheet G, Fig. 135.
With center A and a radius = 27-J" (the largest radius of the
gusset) + 6" (the distance from the center of the boiler to the
center of the gusset C, Fig. 135) = 33-J", draw arc 1.

With center i? and a radius — 26§" (the smallest radius of
the gusset) draw arc 2. Tangent to these arcs draw the

MECHANICAL DRAWING.

straight line I, 2 extended, and through the points A and
draw lines I, A and 2, B per. to I, 2.

Take a point on the per. I, 2, 6 from the point I as a
center and through the point A draw an arc with a radius
= 27*".

ORTHOGRAPHIC PROJECTION. 99

vVith point 2 as a center and 2B as a radius (26%") draw
an arc through B to meet the line 1,2.

Divide both arcs into any number of parts, say 12, and
through these divisions draw lines per. to and intersecting \A
and 2B respectively. Through these intersections draw in-
definite hors. and on these hors. step off the length of the
arcs, with a distance = one of the 12 divisions as follows:

On the first hors. lay off the length of the arc A\' and B\'
=■ Ai and B\ respectively. Then from i' lay off the same
distance to 2' on the second hors. etc. Through these points
draw curves Ai^' and Bi2f. Join points 12' and 13' with a
straight line Then AB12, 13 will be the developed half of
the straight part of the gusset.

On the two ends or front and back of the gusset we have
now to add \" for clearance + 3I" for lap -f- \" allowance
for truing up the plates, total = 5 J" '. And to the sides 2%'
for lap + y allowance for truing up, total = i\" .

The outline of the developed sheet may now be drawn to
include these dimensions with as little waste as possible, as
shown by Fig. 136. Extreme accuracy is necessary in mak-
ing this drawing, as the final dimensions must be found by
measurement.

PROB. 22. — To draw the projections of a V-threaded
screw and its nut of 3" diam. and f" pitch.

Begin by drawing the center line C, Fig. 137, and lay off
on each side of it the radius of the screw \\" . Draw AB
and 6D. Draw A6 the bottom of the screw, and on AB step
off the pitch = f", beginning at the point A.

On line 6D from the point 6 lay off a distance = half the
pitch = f ", because when the point of the thread has com-

IOO MECHANICAL DRAWING.

pleted half a revolution it will have risen perpendicularly a
distance = half the pitch, viz., ■§■".

Then from the point 6" on 6D step off as many pitches as
may be desired. From the points of the threads just found,

B D

Fig. 137. Fig. 138.

draw with the 300 triangle and T-square the V of the threads
intersecting at the points b . . b . . the bottom of the threads.

At the point O on line A6 draw two semicircles with radii

|| the top and bottom of the thread respectively. Divide

these into any number of equal parts and also the pitch Pinto

the same number of equal parts. Through these divisions

draw hors. and pers. intersecting each other in the points as

ORTHOGRAPHIC PROJECTION.

101

shown by Fig. 137, which shows an elevation partly in section
and a section of a nut to fit the screw. Through the points
of intersection draw the curves of the helices shown, using
No. 3 of the " Sibley College Set" of Irregular Curves.

Fig. 139.

PROB. 22. — To draw the proj. of a square-threaded screw
3" diam. and I." pitch and also a section of its nut.

The method of construction is the same as for the last
problem, and- is illustrated by Fig. 138.

PROB. 22. — To draw the projections of a square double
threaded screw of 3" diam. and 2" pitch, and also a section of
its nut.

102

MECHANICAL DRAWING.

The solution of this problem is shown by Fig. 139, and

further explanation should be unnecessary.

Prob. 23. — To draw the curve of intersection that is
formed by a plane cutting an irregular surface of revolution.

Fig. 140.
Figs. 140, 141, and 142 show examples of engine con-
necting rod ends where the curve / is formed by the inter-

tH-tt d:

Fig. 141.

section of the flat stub end with the surface of revolution of
the turned part of the rod.

OR THOGRA PHIC PROJE CTION.

I03

The method of finding the curves of intersection are so
plainly shown by the figures that a detailed explanation is
deemed unnecessary.

Fig. 142.

SHADE LINES, SHADES AND SHADOWS.

Shade Lines are quite generally used on engineering work-
ing drawings; they give a relieving appearance to the projec-
ting parts, improve the looks of the drawing and make it easier
to read, and are quickly and easily applied.

The Shading of the curved surfaces of machine parts is
sometimes practiced on specially finished drawings, but on
working drawings most employers will not allow shading be-
cause it takes too much time, and is not essential to a quick
and correct reading of a drawing, especially if a system of
shade lines is used.

Some of the principles of shade lines and shading are
given below, with a few problems illustrating their commonest
applications.

The shadows which opaque objects cast on the planes of

104 MECHANICAL DRAWING.

projection or on other objects are seldom or never shown on
a working drawing, and as the students in Sibley College are
taught this subject in a course on Descriptive Geometry, it is
omitted here.

CONVENTIONS.

The Source of Light is considered to be at an infinite dis-
tance from the object, therefore the Rays of Light will be rep-
resented by parallel lines.

The Source of Light is considered to be fixed, and the Point
of Sight situated in front of the object and at an infinite dis-
tance from it, so that the Visual Rays are parallel to one
another and per. to the plane of projection.

Shade Lines divide illuminated surfaces from dark surfaces.

Dark surfaces are not necessarily to be defined by those
surfaces which are darkened by the shadow cast by another
part of the object, but by reason of their location in relation
to the rays of light.

It is the general practice to shade-line the different pro-
jections of an object as if each projection was in the same
plane, e.g., suppose a cube, Fig. 143, situated in space in the
third angle, the point of sight in front of it, and the direction
of the rays of light coinciding with the diagonal of the cube,
as shown by Fig. 144. Then the edges a°dv, bvcv will be shade
lines, because they are the edges which separate the illumin-
ated faces (the faces upon which fall the rays of light) from
the shaded faces, as shown by Fig. 144.

Now the source of light being fixed, let the point of sight
remain in the same position, and conceive the object to be re-
volved through the angle of 900 about a hor. axis so that a

ORTHOGRAPHIC PROJECTION.

I05

plan at the top of the object is shown above the elevation, and
as the projected rays of light falling in the direction of the
diagonal of a cube make angles of 45 ° with the hor., then with
the use of the 450 triangle we can easily determine that the
lower and right-hand edges of the plan as well as of the ele-
vation should be shade lines.

This practice then will be followed in this work, viz. :
Shade lines shall be applied to all projections of an object,

Fig. 143.

\R,

/ \

Fig. 144.

considering the rays of light to fall upon each of them, from
the same direction.

Shade lines should have a width equal to 3 times that of
the other outlines. Broken lines should never be shade lines.

The outlines of surfaces of revolution should not be shade
lines. The shade-lined figures which follow will assist in il-
lustrating the above principles; they should be studied until
understood.

Io6 MECHANICAL DRAWING.

SHADES.

The shade of an object is that part of the surface from
which light is excluded by the object.

The Cine of shade is the line separating the shaded from
the illuminated part of an object, and is found where the rays
of light are tangent to the object.

Brilliant Points. — " When a ray of light falls upon a sur-
face which turns it from its course and gives it another direc-
tion, the ray is said to be reflected. The ray as it falls upon
the surface is called the incident ray, and after it leaves the
surface the reflected ray. The point at which the reflection
takes places is called the point of incidence.

" It is ascertained by experiment —

" (a) That the plane of the incident and reflected rays is
always normal to the surface at the point of incidence ;

" (b) That at the point of incidence the incident and re-
flected rays make equal angles with the tangent plane or normal
line to the surface.

" If therefore we suppose a single luminous point and the
light emanating from it to fall upon any surface and to be re-
flected to the eye, the point at which the reflection takes place
is called the brilliant point. The brilliant point of a surface
is, then, the point at which a ray of light and a line drawn to
the eye make equal angles with the tangent plane or normal
line — the plane of the two lines being normal to the surface."
— Davies : Shades and Shadozvs.

Considering the rays of light to be parallel and the point
of sight at an infinite distance, the brilliant point on the sur-
face of a sphere is found as follows: Let AVCV and AhChy Fig.

OR 7 "HO G RA PHIC PR OJE CTION.

107

145, be a ray of light and AvAh a visual ray. Bisect the angles
contained between the ray of light and the visual ray as fol-
lows : Revolve AVCV about the axis Av until it becomes parallel
to the hor. plane at AvClv. At C™ erect a per. to intersect
a hor. through Ch at Cxh join C?Lh (L may be any convenient

Fig. 145.

point on the line of vision), bisect the angle LhAhClh with the
line AhD\ Join ChLh and through the point D\ draw a hor.
cutting ChLh at Df, then AhDlh is the hor. projection of the
bisecting line. A plane drawn per. to this bisecting line and
tangent to 'the sphere touches the surface at the points
B°B* where the bisecting lines pierce it. Therefore R'B11 are
the two projections of the brilliant point.

io8

MECHANICAL DRAWING

The point of shade can be found as follows:
Draw AhG, Fig. 145, making an angle of 450 with a hor.
Join the points E and F with a straight line EF. Lay off on
AhG a distance equal to EF, and join EG. Parallel to EG
Fig. 146. Fig. 147.

Fig. 148,
draw a tangent to the sphere at the point T. Through T
draw TPh per. to AhG. From the point Ph drop a per. to P\
Pv is the point of shade.

Prob. 24.— To shade the elevation of a sphere with graded
arcs of circles.

ORTHOGRAPHIC PROJECTION. IO9

First find the brilliant point and the point of shade, and
divide the radius I, 2 into a suitable number of equal parts,
and draw arcs of circles as shown by Fig. 146, grading them
by moving the center a short distance on each side of the
center of the sphere on the line Bh2 and varying the length of
the radii to obtain a grade of line that will give a proper
shade to the sphere. It is desirable to use a horn center to
protect the center of the figure.

Fig. 149 shows the stippling method of shading the
sphere.

Fig. 140. Fig. 150.

PROB. 25.— To shade a right cylinder with graded right
lines.

Find the line of light E° by the same method used to find
the brilliant point on the sphere, except that the line of light
is projected from the point Bh where the bisection line AhD
cuts the circle of the cylinder.

The line of shade is found where a plane of rays is tan-
gent to the cyl. at Sv and Sh.

Fig. 150 shows how the shading lines are graded from
the line of shade to the line of light.

It will be noticed that the lines grow a little narrower to
the right of the line of shade on Fig. 150; this shows where

MECHANICAL DRAWING.

the reflection of the rays of light partly illumine the outline
of the cylinder.

Prob. 26, Fig. 148. — To shade a right cone with graded
right lines tapering toward the apex of the cone.

Find the elements of light and shade as shown by Fig. 148,
and draw the shading-lines as shown by Fig. 151, grading
their width toward the light and tapering them toward the
apex of the cone.

Fig. 151. Fig. 152.

The mixed appearance of the lines near the apex of the
cone on Fig. 151 can usually be avoided by letting each line
dry before drawing another through it, or as some draftsmen
do, stop the lines just before they touch.

Prob. 2j. — To shade the concave surface of a section of a

hollow cylinder.

Find the element of light
and grade the shading lines
from it to both edges as shown
by Fig. 152.

Fig. 153* Fig. 153 shows a conven-

tional method of shading a hexagonal nut.

ORTHOGRAPHIC PROJECTION.

Ill

SHADOWS.

Let Ry Fig. 154, be the direction of the rays of light
and C an opaque body between the source of light and a

Fig. 154.

surface S. The body C will prevent the rays from passing
in that direction, and its outline will be projected at D on
the surface 5. D is the shadow of C.

The line which divides the illuminated portion of the
surface 5 from the shadow D is called the line of shadow.

Shadow of a Point. — If a line is drawn through a point in
space in a direction opposite to the source of light, the point
in which this line pierces the plane of projection is the
shadow of the point on that plane.

112

MECHANICAL DRAWING.

To find the shadow on the H.P. of a point in space in
the first dihedral angle:

Let A, Fig. 155, be the point in space, and R the
direction of the ray of light; then A" is the shadow of the
point A on H.P., and AHAlH is the hor. proj. and AVAXV the

Fig. 155.

vert. proj. of R. Bv is the point where R pierces V when
prolonged below H.P., and BH is its hor. proj. in the G.L.
The projections of R would then be AVBV and AHBH.

The shadow of a point in V may be found in a similar
manner,

Shadows of Rig J it Lines. — The shadow of a right line on
a plane may be determined by finding the shadows of two of
its points and joining these by a right line; e.g., the shadow
of the line AB, Fig. 156, on H.P. is found as follows:

Through the points AVBV draw the rays AvAlv and BVBXV
to intersect the plane of projection in G.L. in the points A*
and Bxv\ from these points drop perpendiculars to meet rays
drawn through AH and BH in the points A* and BXH. A line
drawn from A/1 to BXH is the shadow of AB on H.P.

If a right line is parallel to the plane of projection its
shadow will be parallel to the line itself.

OR THOGRA PHIC PROJECTION.

If a line coincides with a ray of light, its shadow on any
surface will be a point.

!_L

Fig. 156.

PROB. 28 — To find the shadow of a right line on V.P.
and H.P:

Let AB, Fig. 157, be the given line. Find the shadows

Fig. 157.

MECHANICAL DRAWING.

of the points A and B by passing rays through each of their
projections to make angles of 450 with G.L. The shadow of
AH on H.P. is found at AXH, and that of BH at Bf, where the
rays through these points intersect the H.P. The shadow
oi Av on V.P. is found at^rand that of Bv at BJ, where
the rays through these points intersect V.P. Join AXH and
B* with a straight line and we have the shadow of AB on
H.P., and the shadow on V.P. is found in the same way by
joining with a straight line the points ^rand Btv.

That part of the shadow which falls on V.P. below G.L.,
and on H.P. above G.L., is called the secondary shadow,
because it makes a second intersection, i.e., it is conceived
to have passed through V.P. and made an intersection with
H.P. behind V.P. With the use of the secondary shadow
problems like this are easier of solution.

r "1

c "i >

j \

\d'

■"^f

Fig. 158.

OR THOGRA PHIC PROJECTION.

PROB. 29. — A BCD, Fig. 158, is a square plate parallel to
V.P. ; find its shadow on H.P.

Through the points Ay, Bv, Dv, and AHCH, BHDr\ draw
rays making the angle of 45 ° (or any other angle which may
be adopted) with G.L., and determine the shadows of these
points as explained in Fig. 155. They will be found in the
points A"B", C" , DXH . Join these points with right lines
and they will form the line of shadow of the square plate on
H.P.

PROB. 30. — To find the shadow of a cube on V.P. with
one face in V.P. and the other faces parallel or perpendicular
to H.P.

Fig. 159 shows the cube in the given position. The line
C A DB

Fig. 159.
of shade is composed of edges EF> FG, GD, DB, and the
edges AE and AB in V.P. which coincide with their shadows.

MECHANICAL DRAWING.

The shadow of EF is EVFX, of FG is Fx GXJ of GD is GXDX,
of Z>^ is DXBV. The shadows of the edges AE and .4.5
coincide with the lines. These shadows are found by the
same rules used for finding the shadows of a line in Prob. 28.
The line of shadow is BVD,GXFXFVEVAVDV. The visible line
of shadow is BVDXGXFXEVCVDV.

PROB. 31. — To find the shadow of a rectcmgular abacus on
the face of a rectangular pillar.

Assume the hor. and vert, projs. of the abacus and pillar
to be as shown in Fig. 160.

^ H H

The line of shade of the abacus is seen to be the edges
A"BXH and AXHCXH. The plane of rays through edge AXHBXH
is per. to V.P., and the line AXVEV is its vert. proj. or trace;
its hor. trace is AXHEH . The shadow on the left side face, is
vertically projected in the point Exv where the plane of rays
intersects that face. The ray through the point AXH pierces
the front face in the point EHy which is the shadow of AXH,

OR THO GRA PHIC PR OJE C TION.

117

and ExHEHy Exvev is the shadow of the part FHAlH on this
face.

The line AXHC" is parallel to the front face, therefore its
shadow on it will be parallel to itself and pass through E.

The visible line of shadow is now found to be 1 E^EVHV2 1.

PROB. 32. — Construct the shade of an upright hex. prism
and its shadow on both planes.

Fig. 161 shows the given prism with its line of shade

Fig 161.

AXVBXVEXVDVFV on the vert, proj., CHDHFHEH on the hor.
proj., and its shadow on both planes.

PROB. 33. — Given a circular plate parallel to one coordin-
ate plane ; construct its shadow on the other plane.

MECHANICAL DRAWIXG.

Let AVBVCVDV and AHCH, Fig. 162, be the projections
of the circular plate.

Circumscribe a square EVGV about the circle; its shadow
on H.P. will be the parallelogram AHGH, and the shadows
of the points AVBVCVDV are projected in the points

Fig. 162.

A^B^C^D/1. The shadow of the inscribed circle is an el-
lipse tangent to the parallelogram at the points A"B^CXHDXH \
with B^D^1 and A"C" as conjugate diameters.

The position and length of the axes of the ellipse of
shadow may be found as follows:

Erect a perpendicular at the point Cv making GVKV equal
to radius of the circle- draw KOP; then KP is equal to the
major and MK to the minor axis, and angle 6 is twice the
angle of the transverse axis with the horizontal conjugate
diam. ; i.e., KP is equal to 1, 2, MK to 3, 4, and 2, OxC",
or angle Qy is equal to half KOC v>

ORTHOGRAPHIC PROJECTION.

II9

PROB. 34. — Find the shade of a cylindrical column and
abacus y and the shadow of the abacus on the column.

Let AvBvCv2ind AHBHCH, Fig. 163, be the projections
of the abacus, DHEHFH and DHDVGVFH the projections of
the column.

G-A

Fig. 163.

The line of shade on the column is found by passing two
planes of rays tangent to the column perpendicular to H.P.
and parallel to the hor. proj. of the ray of light. KL and
EH are the traces of these planes tangent to the column at
the points L, and EH and MN the visible line of deepest
shade on the cylindrical column.

The deepest line of shade 1, 2 on the abacus is found in
the same way.

The line of shadow on the column of that portion of the
lower circumference of the abacus which is toward the source
of light is found by passing vertical planes of rays, as 3, 4, to

120

MECHANICAL DRAWING.

determine any number of points in the line, and joining these
points by a line as shown in Fig. 163.

PROB. 35. — Find the shade of an oblique cone and its
shadow on H.P.

Take the cone as given in Fig. 164. Pass two planes of
rays tangent to the cone; their elements of contact will be
the deepest lines of shade. To determine the elements of
contact draw a ray through Cv\ CXH i»s its hor. trace. From

ORTHOGRAPHIC PROJECTION. 121

C" draw lines tangent to the base at D and E; the lines of
contact are CE and CDy and ECD is the line of shade.

The visible line of shade on H.P. is EHDH, and on V.P.
it is CVEV. The shadow on H.P. is EHC,HDH.

PROB. 36. — To draw a front and end elevation of a rect-
angular hollow box with a rectangular block on each face, each
block to have a rectangular opening, and all to be properly
shade-lined and drawn to the dimensions given on Fig. 165.

Draw the hor. center line first, and then the vertical center
line of the end view. About these center lines on the end el-

Fig. 165.
A

Fig. 166.
evation construct the squares shown and erect the edges of the
blocks. Next draw the hidden lines indicating the thickness

122 MECHANICAL DRAWING.

of the walls of the box and the openings through the blocks,
measuring the sizes carefully to the given dimensions.

Draw the front elevation by projecting lines from the va-
rious points on the end elevation, and assuming the position of
the line AB measure off the lengths of the hor. lines and erect
their vert, boundaries as shown by the figure.

PROB. 37. — Given the end elevation of the last prob., cut
by three planes A, B and C, Fig. 166. Draw the projections
of these sections when the part to the left of the cutting plane
has been removed, and what remains is viewed in the direction
of the arrow, remembering that all the visual rays are parallel.

These drawings and all that may follow are to be properly
shade-lined in accordance with the principles given above.

ISOMETRICAL DRAWING.

In orthographic projection it is necessary to a correct
understanding of an object to have at least two views, a front
and end elevation, or an elevation and plan, and sometimes
even three views are required.

Isometric drawing on the other hand shows an object com-
pletely with only one view. It is a very convenient system
for the workshop. Davidson in his Projection calls it the
" Perspective of the Workshop." It is more useful than per-
spective for a working drawing, because, as its name implies
(" equal measures ") it can be made to any scale and measured
like an orthographic drawing. It is, however, mainly em-
ployed to represent small objects, or large objects drawn to a
small scale, whose main lines are at right angles to each other.

The principles of isometrical drawing are founded on a
cube resting on its lower front corner, 1, Fig. 167, and its base

ORTHOGRAPHIC PROJECTION.

123

elevated so that its diagonal AB is parallel to the horizontal
plane. Then if the cube is rotated on the corner 1 until the
diagonal AB is at right angles to the vert, plane, i.e.,
through an angle of 900, the front elevation will appear as
shown at 1, 2, 3, 4, Fig. 167, a regular hexagon.

Now we know that in a regular hexagon, as shown by Fig.
167, the lines lA, A$y etc., are all equal, and are easily drawn

Fig. 167.

with the 300 X 6o° triangle. But although these lines and
faces appear to be equal, yet, being inclined to the plane of
projection, they are shorter than they would actually be on
the cube itself. However, since they all bear the same pro-
portion to the original sizes, they can all be measured with
the same scale.

We will now describe the method of making an isomet-
rical scale.

Draw the half of a square with sides = 2^" , Fig. 168.
These two sides will make the angle of 45 ° with the horizontal.
Now the sides of the corresponding isometrical square, we have
seen, make the angle of 300 with the horizontal, so we will

124

MECHANICAL DRAWING.

draw 14, 34, making angles of 300 with 1,3. The differ-
ence then between the angle 2, 1, 3 and the angle 4, 1, 3 is
1 5°, and the proportion of the isometrical projection to the
actual object is as the length of the line 3, 2 to the line 3, 4.
And if the line 3, 2 be divided into any number of equal parts,
and lines be drawn through these divisions par. to 2, 4 to cut
the line 3, 4 in corresponding divisions, these will divide 3, 4
proportionately to 3, 2.

Now if the divisions on 3, 2 be taken to represent feet
and those on 3, 4 to represent 2 feet, then 3, 4 would be an
isometrical scale of j-.

Fig. 168.

Since isometrical drawings may be made to any scale, we
may make the isometrical lines of the object = their true size.
This is a common practice and precludes the need of a special
isometrical scale.

The Direction of the Rays of Light. — The projection of a
ray of light in isometrical drawing will make the angle of 300
with the horizontal as shown by the line 3, 2 on the front
elevation of the hex., Fig. 167. And the shade lines will be
applied as in ordinary projection.

PROB. 38. — To make the isometrical drawing of a two-
armed cross standing on a square pedestal.

OR THOGRA PHIC PROJECTION.

Begin by drawing a center line AB, Fig. 169, and from the
point A draw AC and AD, making an angle of 300 with the
horizontal. Measure from A on the center line AB a dis-
tance - Ty, and draw lines par. to AC, AD; make AC and
AD 2%" long and erect a perpendicular at D and C, complet-
ing the two front sides of the base, etc.

Prob. 39. — To make the isometrical drawing of a hollow
cube, with square block on each face and a square hole
through each block, to dimensions given on Fig. 170.

As before, first draw a center line, and make an isometrical
drawing of a 2\" cube, and upon each face of it build the
blocks with the square holes in them, exactly as shown in
Fig. 170.

Prob. 40. — To project an isometrical circle.

The circle is enclosed in a square, as shown by Fig. 171.

126

MECHANICAL DRAWING.

Draw the circle with a radius = 2" and describe the square
I, 2, 3, 4 about it.

Draw the diagonals 1, 2, 3, 4 and the diameters 5, 6, 7, 8
at right angles to each other.

Now from the points 1 and 2 draw lines iA, \B and 2A,
2Bf making angles of 300 with the hor. diagonal 1,2. And

Fig. 170.

through the center 0 draw CD and EF at right angles to the
isometrical square.

The points CD, EF, and GH will be points in the curve
of the projected isometrical circle, which will be an ellipse.
The ellipse may be drawn sufficiently accurate as follows :
With center B and radius BC describe the arc CF and ex-
tend it a little beyond the points C and F, and with center A
and same rad. describe a similar arc, then with a rad. which

ORTHOGRAPHIC PROJECTION.
{S

I27

Fig. 173.

Fig. 174.

Fig. 175.

Fig. 176.

Fig. 177.

128

MECHANICAL DRAWING.

Fig. 178.

Fig. 179.

Fig. 180.

Fig. 181.

Fig. 182.

Fig. 183.

ORTHOGRAPHIC PROJECTION. 1 29

may readily be found by trial, draw arcs through the points G
and H and tangent to the two arcs already described.

Prob. 41. — To lay off an angle from a corner of the iso-
metrical cube.

Construct an orthographic square of any convenient size as
shown in Fig. 174, and draw the required angle AOB. From
the corner of the isometrical cube where the angle is to be drawn
lay off along the side a distance equal to OA of the orthographic
square and erect a perpendicular at A. Step off the distance
AB and draw OB the angle required. Any other angle may be
drawn in similar manner.

Figs. 177, 178, 179, 180, 181, and 184 are for practice in
the application of the preceding principles, and at least one

Fig. 184.

•of these should be drawn, or it would be better still if the student
would attempt to make an isometrical projection of his instru-
ment-box, desk, or any familiar object at hand. These figures
may be measured with the ij" scale and drawn with the 2"
scale.

WORKING DRAWINGS.

Working drawings are sometimes made on brown detail-
paper in pencil, traced on tracing-paper or cloth, and then blue-
printed.

The latter process is accomplished as follows'

130 MECHANICAL DRAWING.

The tracing is placed face down on the glass in the print-
ing-frame, and the prepared paper is placed behind it, with the
sensitized surface in contact with the back of the tracing.

In printing from a negative the sensitized surface of the pre-
pared paper is placed in contact with the film side of the
negative, and the face is exposed to the light.

The blue-print system is almost universal in its application
to shop drawings, as evidenced in the report on " Conventions "
found at page 247.

A Working Drawing in the hands of an experienced workman is
intended to convey to him all the necessary information as to shape,
size, material, finish, etc., of a machine or other object that will
enable him to properly construct it without any additional in-
structions. This means that it must have a sufficient num-
ber of elevations, sections, and plans to thoroughly explain
and describe the object in every particular. And these views
should be completely and conveniently dimensioned. The
dimensions on the drawing must of course give the sizes to
which the object is to be made, without reference to the scale
to which it may be drawn. The title of a working drawing
should be as brief as possible, and not very large — a neat,
plain, free-hand printed letter is best for this purpose.

Finished parts are usually indicated by the letter '• f," and
if it is all to be finished, then below the title it is customary
to write or print li finished all over."

Working drawings may be divided into three general types,
viz.: General Plans, Machine Drawings, and Patent Office
Drawings.

General Plans consists of foundation drawings, piping draw-
ings, layout drawings, maps, etc.

ORTHOGRAPHIC PROJECTION. 131

Machine drawings include assembly drawings, detail draw-
ings, diagram and kinematic drawings, sketches and scheming
sheets.

Patent Office drawings must conform to the requirements of
the U. S. Patent Office as published in the " Official Rules of
Practice." They are generally made on two sheet white bristoi
board with black ink. Size of sheet io"Xi5" with a one inch
margin all around. From the top border line of one of the nar-
row edges ij" at least should be reserved for title, number and
date. The signatures of inventor, attorney, and witnesses must
be placed at the bottom of the sheet inside the border line.

COURSE I.
PROBLEMS IN MECHANICAL DRAWING

INCLUDING

LETTERING, GEOMETRICAL DRAWING, ORTHO-
GRAPHIC PROJECTION, DEVELOPMENTS, IN-
TERSECTIONS, AND ISOMETRICAL DRAWING.

COURSE I.

MECHANICAL DRAWING.

MINIMUM NUMBER OF PLATES AND MAXIMUM NUM-
BER OF HOURS ALLOWED TO COMPLETE EACH
DIVISION OF THE WORK.

Note. Registered freshmen conditioned in Mechanical Draw-
ing will be required to complete satisfactorily the following plates
in Courses I and II. In Course I, plates i to 6a inclusive, also
10, ii, 12, 14, 17, 19, and 21 (58 hours). In Course II, plates 22,
23, 24, 32, 33, 34 and 35 (122 hours).

Students conditioned in Mechanical Drawing must work at
least 6 hours per week.

FIRST SEMESTER.

Plates i to 6a inclusive, Freehand Lettering, to be handed in

on or before Wednesday, Oct. 20, 1909. (28 hours.)
Plates 7 to 10 inclusive, Geometrical Drawing, to be handed in

on or before Wednesday, Nov. 26, 1909. (22 hours.)
Plates 11 to 13 inclusive, Orthographic Projection, to be handed
in on or before Friday, Jan. 29, 1910. (24 hours.)
Total, 74 hours.

i35

136 MECHANICAL DRAWING.

Students failing to finish any of the divisions within the specified
time for excusable reasons may make arrangements with the
Instructor to work in one or more extra periods.

SECOND SEMESTER.
Begins Jan. 24, 1910.

Plates 14 to 16 inclusive, to be handed in on or before' Friday,

March 4, 1910. (20 hours.)
Plates 17 and 18, Developments, to be handed in not later than

Friday, April 1, 1910. (16 hours.)
Plates 19 and 20, Intersections, to be handed in on or before

Friday, April 29, 1910. (16 hours.)
Plate 21, Isometrical Drawing, to be handed in on or before
Friday, May 20, 1910. (12 hours.)
Total, 64 hours.
Total number of hours in first and second semesters, 138
hours.

Students failing to complete any of the divisions in the course
in this semester within the specified time for excusable reasons
may make arrangements with the Instructor to work in one or
more extra periods.

Students doing more than the required number of plates in
the given time will receive a higher mark, other things being
equal.

END OF SECOND SEMESTER.

PROBLEMS IN MECHANICAL DRAWING. 137

Directions to be Carefully Observed when Commencing
Work in Mechanical Drawing.

students' conduct in class.

Students will be expected to give strict attention to their
lettering or drawing work during the full time of each drawing
period. Materials and instruments must not be put away until
the warning bell rings.

Nothing should be brought to the drawing table that is not
needed for the drawing work in hand.

If a student expects to be absent from any regular period
he should endeavor to get excused by the Instructor and make
arrangements for making up the work.

A student coming late to class should report at once to the
Instructor, otherwise he will be marked with an unexcused
absence. A report from the Instructor concerning the deport-
ment of each student in class is expected by the Dean every two
months.

When a student is absent from class through an unforseen
cause he should at the next regular period fill out an absence
blank, giving date and cause of absence, sign it, and hand to
Instructor. The work of all absent periods must be made up
by arrangement with the Instructor.

Plate i. Freehand Lettering, Fig. 185, page 138. — Use the 4H
pencil sharpened to a long conical point, not too sharp.

Locate the lower point of the first guide-line 12 squares
from top and 7 squares from left-hand edge of cross-section pad.

Guide-lines should be sketched lightly with a downward
stroke and allowed to remain until letters are approved.

After drawing the guide-lines for the curved letters,
analyze the lines of each curved letter, as given on the chart

i.?8

MECHANICAL DRAWING.

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PROBLEMS IN MECHANICAL DRAWING.

139

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140 MECHANICAL DRAWING.

on the blackboard before attempting to draw the curves
on the pad. A very close approximation of the first
curved letter as it appears on the chart should be
obtained before attempting to draw the second curved
letter.

Do not copy the letters or figures on pages 138 and 142, the
correct form and proportions for all the letters and figures
must be obtained by a careful study of the chart.

The work on all the letters and figures must be strictly
freehand.

Place at the bottom of each plate at the right-hand corner
the following information: Plate number, Section (days and
hours), Time taken to finish plate, and Name, e.g., Mon.
and Wed., 2-4, Plate 1. Time, 4 hours, Name. The
height of these letters should be one square high and all
capitals

Plate 2. Freehand guide lines must .be drawn for all letters
and figures higher than one square and allowed to remain
until letters are approved.

The same care as to proportion and form should be ob-
served in lettering this plate as in Plate 1.

Be careful to balance letters and numbers on all plates
so that the same space will appear from both ends of line
to edge of pad.

The small letters should be extended in width a little be-
yond the proportion given for the larger letters.

The open letters should be spaced closely together and
words should have a liberal space between them, say ij
squares.

PROBLEMS IN MECHANICAL DRAWING. 141

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MECHANICAL DRAWING.

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PROBLEMS IN MECHANICAL DRAWING. 143

Pencil three words only of the small letters at first and
submit for criticism before going on with the others.

Use Ball pen, No. 506, to ink large letters and No. 516
for small letters and figures.

Plates 3-6- — in the next three letter plates the directions for
guide-lines, form, slope, spacing of letters, and for width of
small letters should be carefully observed.

Plate 6.* While a substantial majority of the leading
drafting rooms in the United States are in favor of using Gothic
Capitals exclusively for notes and titles, there are a number
using a combination of Gothic Capitals and Lower Case letters.
So it is deemed wise to introduce one plate of Lower Case letters
to give the student some knowledge of their form, proportion
and construction.

This plate should first be pencilled and after approval, inked.
In addition to the "Ball" pen, No. 516, for large letters, the
small letters should be inked with Gillott's No. 303. All pens
when new should be " exercised" a little before beginning to
letter. The form and proportion of these letters as given by
the largest letters in Fig. 190, on page 145, should be adhered
to as closely as possible.

In general these letters should be made with down strokes
of a uniform pressure. The only exceptions are the letters r

* All letters and figures should have uniform slope. Letters and figures of
one square high should have a full half square slope.

Each plate must be signed by Instructor in charge, in pencil before inking and
in ink when plate is finished. Plates not so signed will be rejected.

When plates are finished and signed they will be retained by the student until
the six plates on lettering are completed, when they are to be bound with paper
binders and handed to the Instructor.

144

MECHANICAL ,

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PROBLEMS IN MECHANICAL DRAWING.

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and u. The curved part of the r imay be made with an up stroke
curved only at the top. The u is made with two down strokes

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and the bottom curve filled in with a stroke to the right and upward.
The m, n, and h should be formed with nearly sharp upper curves.

PROBLEMS IN MECHANICAL DRAWING. 147

This plate will have to be repeated until the desired results
have been obtained.

Plate 6A, Fig. 191. This is an extra lettering plate for those
students who may finish the required plates ahead of time. The
extra plate will increase the grade mark.

GEOMETRICAL DRAWING, INCLUDING CONIC SECs
TIONS; ORTHOGRAPHIC PROJECTIONS; DEVELOP-
MENTS; INTERSECTIONS; ISOMETRICAL DRAWING,
AND ONE WORKING DRAWING.

Before beginning the work in Mechanical Drawing read
carefully the directions given on pages 1 to 17. The size of
the sheet of cream drawing paper will be i5"X2o". This size
will be used for all drawings in mechanical and machine draw-
ing. The border lines and inside divisions will be as shown
on page 148, except where otherwise directed.

Use a 6 H pencil sharpened to a long wedge-shaped point, as
explained on pages 7 and 8.

The lead in the compasses must also be 6 H and sharpened
in the same way. A properly sharpened pencil is necessary
to obtain good work.

When the work has been completely pencilled with fine sharp
lines it should be submitted to the Instructor for approval and
signature, after which the given and required lines of the problem
are to be repencilled with a strong, bold line, using a 4 H pencil
sharpened to a conical point (not too sharp).

Title. The form of title shown in Fig. 192 will be used
on all drawings and should be pencilled and inked together with
the border lines whether the drawing is to be inked or not. All

1 48

MECHANICAL DRAWING.

drawings are to be finished pencil drawings, as directed above,
except where otherwise stated.

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Following is a list of the problems to be drawn on each
plate :

PROBLEMS IN MECHANICAL DRAWING. 149

Plate 7. (Pages 17 to 26 inclusive.)

Problems 1, 2, 3, 5, 6, 7, 9, 11, 13, 14, 15, 16, 18, 19, and
20. Make the dimensions for each problem to suit the given
space so as to comfortably fill it without crowding.

Plate 8. (Pages 26 to 35.)

Problems 21, 22, 24, 25, 26, 29, 30, 34, 35, 37, 39, 40, 41,
42, and 44.

Plate 9. (Pages 43 to 53.)

Problems 54, 56, 57, 58, 59. Use four spaces for problem
59; 70, 71, 72 and 73 in one space each, 63 in two spaces, and
94 in one space.

Plate 10. (Pages 39 to 43.)

Conic Sections. Divide the plate into nine equal spaces.
Draw problems 47 and 48 (in problem 48 draw complete upper
half of ellipse and draw lower half by "Honey's method," prob-
lem 46), 49, 50, 51, 52, 53, and 55. Make twice the size given
in the figures.

Plate ii. (Study pages 74 to 89.)

Orthographic Projection. Divide sheet into nine equal
spaces, as shown in Fig. 193, page 150.

Problem 1 shows three views of a wedge-shaped solid, viz.,
the vertical, horizontal, and profile projections. The vertical
projection is commonly termed the " Elevation" or "Front
Elevation;" the horizontal projection is generally called the
"plan," and the profile projection is known as the "End
Elevation" or "End View."

i;c

MECHANICAL DRAWING.

It will be seen that the end view is obtained by revolving
points projected from the plan to the profile plane through an

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angle of 900 by means of arcs of circles and dropping perpendicu-
lars to intersect horizontals from the same points in the elevation.

PROBLEMS IX MECHANICAL DRAWING.

J5*

Problem 2. This is the same solid placed differently and
having the end view projected by straight lines instead of by
arcs of circles. This method will be adhered to in preference
to the other, as it takes less time.

Problem 3. Given the front and end sections of a rec-
tangular pyramid ih" wideXi" thickX2// high. From the given
views draw the plan.

Problem 4. Given the plan of a pentagonal pyramid whose
side is 1", project the front and end elevations.

Problem 5. Given the plan of an H-shaped block 2" high,
draw front and end elevations.

Problem 6. Given the elevations of a + -shaped block,
draw the plan.

Problem 7. Given front elevation and plan of a hollow
rectangular prism, draw the end elevation.

Problem 8. Given the front elevation of an L-shaped block
2" long, draw the end elevation and plan. In the title of this
sheet leave out the word "Details" and make title name "Ortho-
graphic Projection."

Plate 12.

Problem 1. Given the elevation and plan of a 1}" square
pyramid 1 §" high, draw the end view.

Problem 2. Given the same pyramid of problem 1 when the
plan has been rotated to the left through an angle of 150. Pro-
ject the front and end elevations.

Problem 3. Given the front elevation of the figure obtained
in problem 2 when revolved to the left through an angle of
1 50. Draw the plan and end elevation.

Problem 4. Given the front elevation of problem 1 when

i52

MECHANICAL DRAWING.

revolved through an angle of 300 to the right. Draw the plan
and end view.

Problem 5. Given the end elevation of the pyramid ob-
tained in problem 2 when revolved to the right through an angle
of 1 50. Project the front elevation and plan.

PLATE 12.

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Fig. 194.

Problem 6. Given the end view of the pyramid obtained in
problem 3 when revolved to the left through an angle of 450.
Draw the front elevation and plan.

Problem 7. Given the end view of the pyramid obtained in
problem 4 when revolved through an angle of 300 to the left.
Draw the elevation and plan.

PROBLEMS IN MECHANICAL DRAWING.

J53

Problem 8. Given the front elevation obtained in problem 5
when revolved 300 to the right. Draw plan and end view.
Title similar to that on Plate 1 1 .

Plate 13.

In the same positions as given above draw the projections
of a rectangular prism, Fig. 199, ii"Xi"X2" high.

.biG. 201. Fig. 202.

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Fig. 203.

Fig. 204.

Plate 14.

Fig. 205.

Using same positions as in Plate 12, draw the projections of
a hexagonal pyramid, Fig. 197, circumscribed circle of hexagon
= if" diameter, height if".

154 MECHANICAL DRAWING.

Plate 15,

Given a pentagonal pyramid, Fig. 198, whose side is ij';,
height if", draw the projections of the various positions as
required in Plate 12.

Plate 15 B.

In the same positions as given above draw the projections
of a triangular prism, Fig. 200, page 153, side of triangle ij",
height of prism ij".

Plate 15 C.

In the same positions as given above draw the projections
of a T-shaped block, Fig. 201, page 153.

Plate 15 D.

In the same positions as given above draw the projections of
a wedge, Fig. 202, page 153. Plates 15 B, 15 C, 15 D are extra
plates to be drawn by those who finish the required plates ahead
of time.

Plate 16.

Problem 1. Given the elevation and plan of a hollow tri
angular prism in the position shown in Fig. 203, page 153. Com-
plete the projection in the auxiliary plane.

Problem 2. Given the elevation and end view of a hexa-
gonal pyramid, draw the projection on the auxiliary plane, shown
in Fig. 206, page 153. Use same dimensions given in Fig. 197.

Problem 3. Given the elevation and plan of a wedge, draw
the projection on the auxilary plane, shown in Fig. 205c page 153.
Use same dimensions given in Fig. 202.

PROBLEMS IN MECHANICAL DRAWING.

J55

Problem 4. Given elevation, plan, and revolved position of
plan of a right circular cone, Fig. 212, page 155. Base 3" diam-
eter, height 3". Draw elevation and end view in revolved posi-
tion. See page 88. In planning position of drawings on this plate,

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Fig. 2c6.

Fig. 207. Fig. 208. Fig. 209. Fig. 210. Fig. 211.

Fig. 212.

locate problems 1,2, and 3 along the top of the sheet and problem 4
in the lower left hand.

Plate 17. Developments.

Scheme the layout of all the problems in this plate before
beginning to draw.

Problem 1. Given the elevation and plan of a pentagonal
prism, Fig. 206, page 155, 1" side, if" high, cutting planes A and
B, draw projections as shown in Fig. 125, page 90. Draw the
development of the part below the cutting plane B. See Fig.
126, page 90.

I §6 MECHANICAL DRAWING.

Problem 2. Given elevation and plan of a rectangular pyramid,
Fig. 207, page 155, 2"Xi"Xif" high, and cutting planes A and
B. Draw projections and developments as required for problem 1.

Problem 3. Given views and cutting planes of equilateral
triangular prism shown in Fig. 208, page 155. Draw sections
and development.

Problem 4. Given views and cutting planes of pyramid shown
in Fig. 209, page 155. Draw sections and development.

In this problem when laying out the development, allowance
must be made for the unequal inclined edges of the sides of the
pyramid. See Fig. 117, page 82.

Plate 18.

Problem 1. Given the right circular cone, as shown in Fig.
210, page 155. Draw sectional plan and development.

Problem 2. Given pentagonal pyramid, Fig. 211, page 155,
and cutting planes A and B. Draw sections and development.

Problem 3. Given projections of right circular cone, Fig. 213,
page 155, and cutting planes A, B, C, and D. Draw the projec-
tions of conic sections as indicated by center lines. Draw also
development of part of cone below cutting plane B. If space will
not permit of full development draw half. See Fig. 130, page 95.

Plate 19. Intersections.

Problem 1. Draw three views of two right circular cylinders of
equal diameter, shown in Fig. 214, page 157, intersecting at right
angles to each other, Draw curve of intersection. See page 96.

Problem 2. Make the drawing shown in Fig. 215, page 157,
and draw curve of intersection.

Problem 3. Make drawing shown in Fig. 216, page 157,
and prcjxt curve of intersection.

Problem 4. Fig. 217, page 157, shows a square prism inter-

PROBLEMS IN MECHANICAL DRAWING
Fig. 214. Fig. 215.

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Fig. 217.

158 MECHANICAL DRAWING.

sected by a hexagonal prism partly shown in elevation. Com-
plete the elevation and draw also half end view. Total length
of hexagonal prism 4§".

Plate 20.

Problems 1 and 2. Construct the curves of intersection
shown on the connecting-rod ends in Figs. 140 and 141, page 102,
and draw three complete views of each.

Problems 3 and 4. Draw the projections of a "V" and
"Square" threaded screw according to directions given on pages
99 and 100, Figs. 137 and 138.

Plate 21. Isometrical Drawing.

See pages 122 and 123.

Problem 1. Make the isometrical drawing of a 2 J" cube.
Draw a 2\" isometric circle on the upper face by the method
shown in Fig. 171, page 127. From the lower left-hand corner
of the right-hand face lay off angles of 150, 300, and 450. Use
method shown in Fig. 174, page 127. See problem 41, page 129.

Problem 2. Draw the hollow cube as shown in Fig. 170,
page 126, except that instead of the hollow block on the upper
face draw a cylinder of if" diameter and 1" high.

Problem 3. Make the isometrical drawing of a hexagonal
headed bolt, shank 1" diameter and 2" long. Head 1" thick.
Use either of the methods shown in Figs. 173 and 175, page 127.

Problem 4. Make the isometrical drawing of a pentagonal
prism of i|" sides and 2 J" high. On the top of the prism draw
an isometric circle of 2" diameter. See Fig. 176, page 127.

Problem 5. Make the isometrical drawing of the tool box
shown at Fig. 183, page 128. Dimensions 3 \" long X 2" wideX 1"
deep, over all. Cover and sides \,} thick. Use the method of

PROBLEMS IN MECHANICAL DRAWING.

J59

offsets shown in Fig. 182, page 128. Place full dimensions on
this drawing. Plate 21 is to be finished in pencil and inked.
See directions for inking with the spring bows on page 14, the

PLATE 22.

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large compass on page 13, and the ruling pen on page 9. See
also directions given for inking Plate 22 on page 159.

Plate 22. Working Drawing.

Problems 1 and 2. Make the working drawing of connecting
rod and axle shown in Fig. 218, page 159. Begin by laying off
the border line and space for title. Draw guide-lines \" high
and \" space between lines. Locate all center lines of rod and

t6o

MECHANICAL DRAWING.

axle. Use 6 H pencil sharpened as directed on page 8. Draw
fine, clear, clean-cut lines. When drawings of rod and axle

are complete and approved, strengthen the lines with 4 H pencil,
conical point. Then draw dimension lines. Next put in arrow-

PROBLEMS IN MECHANICAL DRAWING. 161

heads and dimensions, beginning at the upper left hand and
working down toward the lower right-hand corner.

When the drawing is properly finished in pencil and signed
by the Instructor it will be ready for tracing on cloth. Begin
the tracing with the spring bow pen. Ink all arcs of circles,
circles, and irregular curves before inking any straight lines.
Then ink dimension lines. Next ink arrow-heads and dimen-
sions in consecutive order, beginning with the left-hand arrow-
head, then dimension, next sign of inches, and then left-hand
arrow-head. Ink hatch lines and center lines last of all. For
weight and character of lines see Standard Lines on page 247.

Plate 22 F.

Problem 1. Make drawing of automobile crank axle, as
shown in Fig. 219, page 160. Use same directions for pencilling
and inking as given for Plate 22.

Problem 2. Make drawing of top bracket for planing ma-
chine, as shown in Fig. 219, page 160. Project also right end
view of bracket. Make finish pencil drawing and trace on cloth.

This plate is not required in the course of mechanical draw-
ing, but credit will be given for it in the Freshman Course to those
who may have time to finish it in this course. A higher mark
will be given to the student completing this plate in addition to
the required plates.

Course I is preparatory to Courses II and III.

Course III is given in " Mechanical Drawing and Elemen-
tary Machine Design," by John S. and D. Reid, John Wiley
& Sons, New York.

CHAPTER VI.

ARCHITECTURAL DRAWING.

The method of applying the principles of projection to the
making of architectural working drawings is the same as in me-
chanical or machine drawings, except that third angle projec-
tion is used in the latter, while first angle projection is almost
invariably used in the former.

The instruments and materials used in architectural draw-
ing are practically the same as for mechanical and machine
drawing. There are a few additional materials needed however,
in architectural work, viz., a tinting brush, water glass, color
saucer, colors, stick of India ink, slate, ink well, and white draw-
ing paper suitable for taking water colors.

While it is true that experienced architectural draftsmen
use pencils of a much softer grade than those used by machine
draftsmen, it is better for the student while learning to continue
the use of the harder grades as required in mechanical
drawing.

The following objects which have been selected for problems
in architectural drawing in addition to those which have been
given before are necessarily limited. They are elementary and
preparatory to a larger and more comprehensive course in architec-
tural drafting.

162

ARCHITECTURAL DRAWING.

I63

164 MECHANICAL DRAWING.

FRAMING JOINTS.

In elementary building construction, carpenters' joints occupy
an important place. The joints are divided into various forms
of notches, tenons, and mortises and combinations of the same.

A Single Notch is a hollow cut in a board or scantling into
which another board is fitted and fastened. Examples of the
single and double notches are shown in Figs. 220, 221, and 222,
Plate 23.

The Butt Joint. — Fig. 223 shows a butt joint where the end
of a stud is fastened to a plate without a notch.

End Lap. — Fig. 224 is a special form of double notch usually
called halving. The boards are of equal thickness and both
are notched half their thickness, so that when fastened together
they form a smooth flush surface.

Beveled Lap. — Fig. 225 is an example of the lap joint when
the notch in both scantlings is beveled with an equal and opposite
slope. Fig. 226 shows a lap joint where the pieces cross each
other.

Dovetail Halving. — Fig. 227 shows a dovetail lap joint where
notches are of such slope that the end cannot be withdrawn.

Mortise and Tenon. — Fig. 229 shows a plain mortise and
tenon joint. The tenon, A, is the projection on one piece which
is made to fit into the mortise shown, cut in the other with two
wedges which are driven in when the tenon is in place to tighten
it. The shoulders of the tenon are shown at its root; the abutments
of the mortise are the faces on which the shoulders rest; and
the cheeks are the two internal faces on which the grain runs
lengthwise. The tenon is made one-third the thickness of the
scantling. The finished joint is shown at B.

ARCHITECTURAL DRAWING

I65

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l66 MECHANICAL DRAWING.

Mortise and Tenon Joggled Joint. — This joint, Fig. 230, is
a modification of the preceding one to suit the angle at which
the timbers are inclined. The left hand end of the tenon is cut
square to the plane of the abutment to avoid the sharp end which
would tend to shear the timber beyond. The angle at A should
be a right angle. An orthographic projection of this joint is
shown at B.

Straddle or Bridge Joint. — This joint, Fig. 228, is a reversal
of the mortise and tenon joint

Splice or Lap Joint. — Fig. 231 shows a simple lap splice
used to join two timbers together.

Scarfed Joint. — Fig. 232 shows a scarfed joint to resist cross
stress. A fish plate added would strengthen this joint very much.
The compression part should have a square abutment as shown,
but the tenon part may have a bird mouth abutment and sally.

Iron Fish Plate Joint. — Fig. 233 shows the two beams butted
end to end, and iron fish plates are bolted on to two opposite sides
and sometimes to all sides for compression.

BRICKWORK.

In building a wall with brick the main object is to obtain
the greatest strength with the materials used, and at the same
time to obtain the most pleasing external appearance. The
most important methods used to obtain these results are what
is known as the English and Flemish bond. By bond is meant
the connection of bricks' one with another by lapping them over
each other in building.

Fig. 234 is an example in English bond where the courses
appear as heading and stretching courses alternately.

ARCHITECTURAL DRAWING. 167

Fig. 235 shows an example of the Flemish bond where the
headers and stretchers alternate in the same course.

Brick and Cement Foundations. — The width of the lowest
course of a wall must be such that it will not press in the ground
with a greater load per square foot than the ground can safety
bear. This is accomplished by what is known at footings, whose
widths should be apportioned to the weight to be carried, so that
there will be a uniform pressure under all parts of the building.
An empirical rule is often used which makes the lowest course
of the footings twice the width of the wall itself. Footings are
always made in English bond, and spread on each side of the
wall by one-quarter brick at each off-set. The outer rows should
be headers as far as possible.

Concrete is often used nowadays to lessen the pressure per
square foot on the earth below. Quite often the footings are
dispensed with, and the wall is built directly on the concrete
foundation. Fig. 236 shows a sectional elevation of a brick
footing with a concrete foundation.

Stone Foundation Wall. — There are three classes of walling,
viz., rubble, regular course masonry, and ashlar. A proper bond
is always desirable. This is obtained by using headers and
stretchers similar to brickwork, but not necessarily so regular.
Headers are long stones extending into the wall from either face
and reching beyond the middle of the wall.

Fig. 237 gives an example of a stone foundation wall. Fig.
238 regular course masonry, and Fig. 239 rock face, plain and
chamfered ashlar.

Fig. 240 shows two segmental arches which have for their
intrados segments of circles. The names of the different parts
are given on the drawing.

1 68 MECHANICAL DRAWING.

ARCHITECTURAL LETTERING.

More latitude is allowed to the architectural draftsman in
his choice of styles of lettering for notes and titles on working

PLATE 25.

■1

)H ,

* * -s -» 1

"xt;

■

( sj/i5>

.:==*.=■

v— pi—

--^-^

Fig. 241.

drawings than is given o the machine draftsman. The latter
is required to use that style of letter which gives the neatest

ARCHITECTURAL DRAWING.
PLATE 25.

169

■

N*«

7f5k \

7>?f "'

T \SMfi

t ?C3

t-,/3?^

- >**"^"^' .

/ " r^ \^^b

1 \ ij^w

^^m

^^B

^^m

mlf

^^rl /

mB \ '

JKmmmmmf

Fig. 242.

170 MECHANICAL DRAWING.

appearance with a maximum of legibility and requires the least
amount of labor and time to construct it; while the former is
expected to use a style of letter suggested by the character of
the drawing to be named and noted.

The alphabet shown in Figs. 241-242, known as the classic
Renaissance letters, is selected as a good form of letter for general
purposes, where a Roman letter would be suitable for the work
in hand. This alphabet was originally designed by Albrecht
Durer and adopted by Frank Chouteau Brown, in his treatise
on "Letters and Lettering," Bates & Guild Company, Boston.
Mr. Brown's book is recommended to those students who desire
to follow up their studies in architectural lettering.

The method used for the instrumental construction of these
letters is similar to that used in the Roman letter given on page 67.

For the purpose of learning the form and proportions of
these letters the alphabet should be drawn mechanically to a
scale as large as convenient; after which practice should be had
by forming the letters freehand to smaller sizes, until the student
becomes familiar with their construction.

ARCHITECTURAL DRAWING. 171

ORDERS OF ARCHITECTURE.

There are, generally speaking, five orders of architecture,
the Tuscan, the Doric, the Ionic, the Corinthian, and the
Composite, but in reality there are only three, because the
Tuscan may be regarded as a simplified Doric, and the Com-
posite as a Corinthian modified by the Romans in an endeavor
to surpass the Greeks. (Vignola.)

Tuscan Order. — Fig. 243 shows the pedestal, base, entablature,
and capital of the Tuscan order. The dimensions are given in
inches, but the drawing may be made by using a scale of modules
given in the figure.

A module is an arbitrary term for a unit of measure or pro-
portion partie, or minute, is an arbitrary division of the module.
Vignola divides the module for the Tuscan and Doric orders
into twelve parts.

The technical names given to the different parts are given
in the figure.

Doric Order.— Fig. 244 shows the entablature and capital
of the Doric order according to Vignola, The proportions are
given in modules and parties. The technical names of some of
the details are given in the drawing.

Fig. 245 shows the elevation and plan of the entablature of
the Doric Order. Fig. 246 gives the complete Order.

Ionic Order.— In Figs. 247-248 are given the pedestal, base,
capital, and entablature with some of their details. The propor-
tions are given in modules. See Prob. 59, page 45, in connection
with the drawinsr of the volute.

172

MECHANICAL DRAWING.

ARCHITECTURAL DRAWING.
PLATE 27.

173

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Figs. 245-246.

174

MECHANICAL DRAWING.

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CHAPTER VII.
ARCHITECTURAL DESIGN.

In this chapter are given some notes and suggestions on the
design and construction of a modern American dwelling house,
to be followed with the plans and specifications of a concrete
example showing the practical working drawings prepared by
Brown Bros., architects, Cedar Rapids, Iowa.

Each student will be expected to modify this design and pro-
duce the plans and specifications of a dwelling distinctly different
in interior arrangement and exterior design, using the given
drawings as suggestive examples only.

Sketches.

When about to prepare drawings of a dwelling for a customer
the architect must acquaint himself with all the conditions con-
nected with the problem.

The location of the lot and its size, the amount of money
available for the completed house, and the ideas of the customer
as to number and size of rooms, interior arrangement and exterior
design, etc. When these are learned he will prepare a sketch
and submit it for approval, when the sketch for the general
arrangement and design has been agreed upon.

Working Drawings.

The working drawings can be made and the specification
and contract drawn up ready for signature. When the contract

*75

176 MECHANICAL DRAWING.

is signed the architect will prepare the full-size detail working
drawings, placing as many as possible on one sheet to facilitate
the reading of the same by the workmen.

The scale of \" equal to 1 foot is generally used in making
the plans and elevations, but of course this varies according to
conditions.

SPECIFICATIONS

FOR ALL LABOR AND MATERIALS REQUIRED IN THE ERECTION AND COMPLETION OF

A FRAME RESIDENCE

FOR

MR. GEORGE M. VERITY,

TO BE BUILT AT
MIDDLE TOWN, OHIO.

ALL WORK AND MATERIALS TO BE IN STRICT ACCORDANCE WITH ACCOMPANYING

DRAWINGS AND THE FOLLOWING SPECIFICATIONS, PREPARED FOR

THE PURPOSE BY

BROWN BROTHERS,

architects.

808-9 Security Savings Bank Building, Cedar Rapids, Iowa.

General Conditions.

The owner reserves the right to accept or reject any or all
bids. The work is to be laid out by the contractor, who will be
responsible for its correctness. A competent foreman is to be
kept at the building during all working hours to receive and carry
out the orders given by the superintendent.

The following specifications and the above mentioned draw-
ings are intended to correspond and be illustrative of each other,
and any part of the work that may be mentioned in the specifica-
tions and not shown on the drawings, or vice versa, is to be executed
the same as though it had been particularly mentioned and shown

ARCHITECTURAL DESIGN.

177

PLATE A.

DdSfmrol Moor- Pldfj

Fig. 249.

Residence for G. W. Wilson, Champaign, 111., Brown Brothers, Architects, No.
808-9 Security Savings Bank Bldg., Cedar Rapids, Iowa.

178 MECHANICAL DRAWING.

in both. No deviations are to be made from the drawings or
specifications without the written consent of the owner and
architect. If any work is, in the opinion of the superintendent,
executed in a slight or unsound manner, the same shall on his
orders be immediately pulled down and made right at the sole
expense of the contractor. None but the most skillful work-
men are to be employed on the work and any mechanic or laborer
employed thereon who, in the opinion of the superintendent,
shall prove careless or incompetent, shall be immediately removed
therefrom by the contractor when notified to do so by the super-
intendent. No part of the work is to be done as "piece work,"
nor let to a sub-contractor, without the consent of the owner.
All materials required for the execution of the work to be fur-
nished by the contractor, unless otherwise specified, must be
of the very best quality of their respective kinds, and to be properly
applied at times as directed by the superintendent.

All work is to be done in a substantial and workmanlike
manner, and if any difference of opinion shall arise as to the
quality or quantity of workmanship or materials or upon any
other matter connected with the building, the contractor must
in all cases be bound by the decision of the architect or super-
intendent. The superintendent may cause to be removed at any
time before the acceptance of the work any materials or workman-
ship that does not comply strictly with the requirements of the
plans or specifications, or in the event that such removal might
cause damage or injury to the other portions of the work, or if the
contractor neglects or refuses to remove same, then the architect
or superintendent may deduct from the amount of the contract price
a sum that in his judgment shall be just and reasonable as a
set-off to the injury to the building caused by non-compliance

ARCHITECTURAL DESIGN. 179

with the requirements of the specifications, as well as for the
difference of value between the specified and the inferior work-
manship or materials, and give his certificate only for the
balance that may be due the contractor. The architect shall
have full power to have the work pushed forward, and in default
of the compliance by the contractor with the terms of a notice
to that effect within three days of the service of the same, the
architect shall have full power to enter the premises and entirely
stop the work, and exclude the contractors therefrom and to
furnish all materials necessary, or to use materials then on the
premises, or to employ any other workmen to finish such work
that may remain unperformed or unfinished, and charge the
amount of such unfinished or unperformed work to the original
contractor, with all other expenses or costs that may accrue
by reason of said change, and to have full power to retain the
amount of such costs and expenses out of any moneys
that may then be due or coming due from the original con-
tractor.

The contractor shall thoroughly scrape and sweep the floors
throughout and remove all rubbish from the premises; also see
that all sash, doors, locks, etc., are in proper working order,
and shall furnish the proper keys for all locks and leave the entire
building ready for occupancy.

Staking Out.

Contractor must stake out the building, and he must establish
all levels and pay all charges for engineer, if services of an engineer
are found to be necessarv.

180 MECHANICAL DRAWING.

Bond.

The contractor will be required to furnish a surety bond
acceptable to the owner, and be ready to sign contract and execute
bond within three days after date of the acceptance of his bid,
bond to be equal to fifty (50%) per cent of the amount of the con-
tract. A certified check for dollars ($ ) must accompany

each bid as a guarantee that contractor will sign up at his figures
within three days after bids are opened, otherwise check is for-
feited to owner.

Permits.

Contractor must obtain and pay for all building permits
and street permits, and comply with local building ordinance in
every respect. Proper danger signals must be maintained at
night and barriers erected to protect the public from accidents.
Should any accident occur by reason of neglect on the part of
the contractor, he will be held personally liable for same.

Excavations.

Excavate for all walls and piers to a depth as shown on the
several drawings and sections. All trenches must be of the
depth as shown, and the bottom of all excavations must be per-
fectly level before any masonry work is commenced in same.
All dirt not needed on the premises is to be carried away at the
expense of the contractor only after having received an order
to do so from the owner. The grades are shown on the drawings
and the contractor is to be governed by same in making his calcula-
tions. In taking the dirt from the main excavations the loam
is to be stacked in one place and the under soil in another, so

ARCHITECTURAL DESIGN.
PLATE B.

181

»°j &r*

w.J A,, 1a.

fTr^r fWr PU

Fig. 250.

Residence for G. W. Wilson, Champaign, 111. Brown Brothers, Architects, No.

808-9 Security Savings Bank Bldg., Cedar Rapids, Iowa.

182 MECHANICAL DRAWING.

that when grading is done the black loam can be placed on top
again. All trenches and cellar bottoms are to be thoroughly
drained of all water before any masonry work is commenced.
The grading back of dirt that has been thrown out of excavations
will be done by another contractor or agreed upon with owner
in this contract.

Masonry Work.

All walls, piers, chimneys, etc., in basement and wherever
shown on plans and elevations are to be of concrete, or of good
hard-burned merchantable brick, laid in lime mortar, as shown by
the plans and sections. Submit alternate bid on brick walls. All
concrete to be made of good Portland cement (Atlas or its equal,
subject to the approval of the architect) and good coarse gravel
(or crushed rock in size to pass through a 2" ring) and clean,
sharp sand. Proportions to be as follows: one part of cement,
six parts of gravel or crushed rock, and three parts sand. If
gravel is used in place of crushed rock, omit the two parts of
sand from mixture. All to be thoroughly mixed dry on a board
platform and then mixed with water to the proper consistency.
All concrete must be kept thoroughly wet for at least two days
after having been placed in the forms. Forms to be made of
rough plank sides of inch lumber and to be firmly braced and kept
in place until the concrete has properly set. Build in all pipes
through concrete walls as work progresses. All exposed face
brick to be Twin City Brick Co.'s (or its equal) oriental brick,
Minneapolis, Minn, (medium and dark shades, one-half of each),
and to be laid up with \" mortar joints and raked out \" deep.

Build chimneys and fireplaces as shown on drawings, sections
and details of materials as marked on drawings and line all smoke

ARCHITECTURAL DESIGN.

i83

PLATE C.

T>oor«,

Ail

F-loo^ A'Vn>*i Dint-

uj «... ~

— G)cCOoJ floor H^p-K

Residence for G. W. Wilson, Champaign, 111. Brown Brothers, Architects, No.
808-9 Security Savings Bank Bldg., Cedar Rapids, Iowa.

1 84 MECHANICAL DRAWING.

flues with fire-clay flue linings, All chimney work to be laid
up with lime mortar with a little cement added. Turn dis-
charging arches over' each fireplace and support heads of all
square openings of fireplaces with H. W. Covert's cast-iron throat
and damper, with four (4) inch bearing on walls at front, back and
ends. Place thimbles in all chimneys where directed by su-
perintendent. For design of mantel, see details. Line all fire
openings with fire-brick laid in fire-clay mortar.

Cistern. — Provide and put in a 100 bbl. cistern where directed
by the owner. This cistern is to be built of good hard-burned
merchantable brick 4" thick, laid in cement mortar for bottom,
sides and arched top, and to have a \" smooth coat of cement
mortar (one part cement to one of sand) for the finished surface of
walls and bottom.

Cistern is to be circular in plan and to be about 8' in diam-
eter by the proper height to contain 100 bbls. of water. Provide
a filter wall on a slight curve in center of cistern, and to extend
to within 18" of the top. This filter wall is to be laid up of one
course of brick without any mortar. Provide a cast-iron rim 28"
in diameter by 6" high to finish off the top, and also provide a
cast-iron cover with 3" ring.

Top of cistern cover to be about 12" below finished grade of
house when completed. Make all proper connections from water
pipes leading from down spouts to the cistern, and have all pipes
from down spouts enter cistern wall on same side of filter wall.
Provide opening in cistern wall to receive the pipe from water
lift and connection to hot water heater. Provide 6" vitrified
salt-glazed sewer pipes with cemented joints to connect up with
all down spouts and cisterns and lay same at least 2' 6" below
finished grade of house. Provide a fall of at least \" to

ARCHITECTURAL DESIGN. 1 85

the foot for all pipes. These sewer pipes are to extend 8" above
finished grade line at each down spout, and to be thoroughly
cemented around all spouts. Provide proper overflow pipe to
cistern and cutoffs for down spouts at ground.

Water-Proofing of Walls. — Cover the exterior surface of all
outside basement walls from bottom of footings up to finished
grade line and over top of wall at this level with one coat of hot
asphaltum or dehydratine.

Cement Work.

Over entire basement floor and wherever marked " cement
floor" on plans, is to have a cement floor consisting of 3"
bed of concrete, composed of one part of Atlas Portland cement
to six parts of crushed rock and three parts of clean, sharp bank
sand. Top coat to be \" thick, composed of one part of same
cement as above specified to two parts of clean, sharp bank
sand, troweled to a perfectly even and polished surface and lined
off in squares approximately 48X48".

Lathing.

All stud walls, partitions and ceilings or first story are to be
lathed with No. 1 pine, spruce or yellow poplar lath, free from
red knots or bark, and well seasoned; break joints at least
every 18". Place lath §" on the ceilings and but very little
closer on the stud walls. No lathing through the angles
allowed; all walls to be made solid by the carpenter before
lathing begins.

Half green lath are preferred, but if bone dry, wet the lath
well before plastering.

i86

MECHANICAL DRAWING.

PLATE D.

-*~^'Jy

rut.. Mitv-.A-s.ju.

'rw,™*'--., i.l.tb/'iw,.

fc)

•r

Fig. 252.
Residence for G. W. Wilson, Champaign, 111. Brown Brothers, Architects, No. 808-9
Security Savings Bank Bldg., Cedar Rapids, Iowa.

ARCHITECTURAL DESIGN 187

Plastering.

Plaster all interior wood lath with " Adamant" patent wall
plaster (or its equal "Universal,") to be put on according to the
printed instructions of the manufacturers. Plaster to come to the
building ready mixed with nothing but the water to be added.
This is to be two-coat "drawn work," and all walls and ceilings
are to be given a hard, smooth plaster-of-paris finish in the
universal white finish (all for papering).

Use f" grounds around all openings for interior work for
baseboards, wood strips, etc., in the building. All plaster must
come up flush with grounds and be roded perfectly straight, true
and plumb.

All patching of plastering to be done by the plasterer after all
woodwork is complete. Plasterer to clean out all his rubbish
and scaffolding from the buliding when his work is completed.

Plaster Wainscoating.

The walls of kitchen, bath and toilets are to have a good patent
plaster wainscoting — Keene's Best Cement or its equal — 4' 6"
high; to be two-coat work. First coat to be a scratch coat;
second coat to be troweled to a perfectly smooth, even and
polished surface.

Timbers. — All timbers, girders, trimmers, joists, truss beams,
partitions, studs, rafters, etc., must be prepared, framed and con-
structed according to the drawings and sections. All floor joists
properly sized to widths and jointed, crowning on top edge.

All "piece stuff" to be clear Georgia, Arkansas or Northern
pine.

Joists and built-up girders to be of a size as shown on plans.

All joists placed sixteen (16) inches on center.

1 88 MECHANICAL DRAWING.

All built-up girders to be well spiked together.

Bridging. — Cross bridging to be made of sound stuff 2 X 2",
well fitted, put in as soon as joists are leveled, and spiked with
two iod. nails at each end. Joists from 5 to 8' bearing one row
12 to 18', two rows of bridging.

Headers and Trimmers. — To be double thick, well framed
and spiked together, leaving all openings of sufficient size for
finish of stairs, chimneys, etc., and in no case closer than 5"
to the inside of any smoke flue. All openings in brick or
concrete to have wooden lintels or brick arches, not less than
4" thick, by the required width to cover the thickness of wall.
Build in all "wood brick" in brick walls where necessary for
nailing.

Partition and Wall Studs. — All studs to be 2X4" set 16"
on center and doubled and trussed at all openings where re-
quired, in substantial manner. Partitions to be sized and jointed,
set plumb and straight. All angles of rooms made double and
solid. All bearing partitions, and partitions over 6' in length
to be bridged horizontally once in height. All studding to have
2 X 4" bearing plates top and bottom.

Closing up Doors and Windows. — When building is ready
for plastering, all sash and glass is to be in place, and contractor
is to have temporary doors and locks for all outside doors.

Sheathing. — Enclose the entire house, sides and gables with
D. & M. fence flooring, f X6" yellow pine. Roof sheathing to
be JX6" S. O. S. No. 2 boards, yellow pine, laid open 2",
properly nailed to every studding and rafter with two nails to
the board. Tight sheathing to extend from bottom of studs clear
up sides of house and into all gables. Open sheathing on roof
cnly. Fill in between outside studding of bathroom with saw-

ARCHITECTURAL DESIGN.

189

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190 MECHANICAL DRAWING.

dust or shavings and pack firm. Cover all sheathing on walls
and gables with heavy tarred felt paper well tacked on and
fill in between studs of oustide walls with same felt as above
specified, so as to leave a double dead air space between
sheathing and plastering.

Roof. — The carpenter shall frame and construct, according
to the drawings, sections and specifications, in the most thorough
manner, all roof rafters, hips, ridges and valleys.

Shingles. — Where shown on drawings on roof and sides to
be first clear red cedar shingles, 5 to 2" and laid 4^" to the weather,
with two 3d. cut iron nails to each shingle. Make perfectly
water-tight around all chimneys, skylights, scuttles, etc., gutters,
fire-walls or wherever the roof of one part joins the perpendicular
walls of another, with flashings. (See tin and galvanized iron
specifications.)

All proper bond timbers, cradles for arches, etc., and wooden
brick of every description necessary for the proper execution of
the work to be furnished by the carpenter ; also all lumber necessary
for lookouts, decks and furring for the tinners, galvanized iron
work, etc. ; also build all necessary scaffolding to do the carpenter
work properly.

Cornice. — All exterior wood finish to be construted in strict
accordance with details and to be of thoroughly seasoned clear
cypress. Provide bed mould and beaded ceiling for soffit of all
cornices.

Porches. — Build all porches as shown on the plans, elevations
and details. Use rough posts, timbers, barge boards, brackets,
casings, etc., for all exterior woodwork except sash, doors and
frames. Furnish and put in place a 2 J" crown mould all around
edge of ceiling to finish same against wall. Porch ceilings to

ARCHITECTURAL DESIGN.

191

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192 MECHANICAL DRAWING.

have "V" edge and center ceiling to be JX6" clear Washington
fir or cypress.

Windows. — All windows for this building must be of the forms,
style and dimensions as marked on plans, elevations, sections
and details, or as hereinafter described. All pulley stiles to be
J" thick, of clear yellow pine and provided with best noiseless
cast-iron ball-bearing axle pulleys (wheels in one solid piece).
Sash hung to solid braided Silver Lake " A" or " Sampson Spot"
sash cord and cast-iron weights. Use lead weights where necessary.
Sash to be of clear seasoned white pine if" thick and to have
extension ends to side rail of upper sash for all double-hung win-
dows.

All casement sash hinged at side to swing out. Screen sash
on casement windows, hinged at side to swing in. All windows
to be equipped with Chamberlain's metal weather strips all
around.

Frames. — All frames to be made of J" pulley stiles, \" head
of clear yellow pine, and i f " sills of clear Washington fir or cypress.
Door frames for outside doors if" thick and rabbetted; same
material as above. Inside door frames J" thick of same wood
as finish of rooms, and use wood stops \ XiJ" with moulded
edge. (See details.)

Plank Frames. — Basement frames to be of clear cypress or
Washington fir if" thick. All frames must come to the build-
ing primed with white lead and linseed oil, one coat. Basement
window frames to have clear Washington fir or cypress sills
if" thick.

Floors. — The first story joists will first be covered with f X
6" D.&M. fence flooring, yellow pine. Finished floors of living-
room and dining-room to be quarter-sawed clear yellow pine.

ARCHITECTURAL DESIGN. 193

iX2¥' face, T. & G. sides and ends, and no boards to be less
than 4" long.

All finished flooring to be first clear JX2^' face, T. & G.
sides and ends, well secret-nailed to every joint. All other floors
except as above specified to be clear quartered Arkansas or
straight-grained Oregon pine, |X4i", T. & G. sides and
ends.

Finished floors must be planed and scraped before staining
or varnishing. All floors must be well protected before varnish-
ing, until house is entirely completed. Then staining and varnish-
ing to be done the last thing. No finished floors to be laid until
all other workmen except painters are through.

All under floors to be laid diagonally and end joints cut on
a line parallel with joists, and to lap half the thickness of joists
and well nailed with two nails to each end of the board and with
twb nailings on each intermediate joist.

Porch floors, unless marked "cement" on plan, to be JX4"
clear-matched Washington fir or cypress, laid in white lead,
and well drawn up and nailed to every joist.

Grounds. — Put up grounds for the finish of all windows, doors,
bases, casings, wainscoting, etc., before plastering. Those on
wooden partitions to be f X ij"; on brick walls, f X ij".

Closets. — All closets finished with two shelves to each unless
otherwise shown on details and plain wood strips extending
around closets JX4" wide on which to fasten clothes hooks. All
pantry and kitchen cupboards to have plain doors (no panels),
f" thick, and to have shelves 12" apart, set on adjustable
wood strips with cast-iron pin adjusters. Below counter shelves
provide drawers, bins and doors as marked on plans. All drawers
to have center oak guide strips underneath. Glass doors to

i94

MECHANICAL DRAWING.

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ARCHITECTURAL DESIGX. 195

cupboards where shown to be AA double strength clear glass,
put in with wood stops nailed in place.

Wainscoting. — No wood wainscoting in the building.

Doors. — All doors must be made of material same as standing
finish of the rooms in which they occur, thoroughly seasoned,
and of the sizes marked on plans, fitted in their respective
places, hung and trimmed complete. All doors, except as otherwise
shown, to be fine cross panel O. G. stock doors. Xo veneered
doors in house.

All cupboard doors to be plain, §" thick (no panels). All
glass doors to be glazed as shown on drawings, with D. S. clear
glass unless otherwise marked. Picture mould in all rooms and
halls except kitchen, bathroom and pantry of same wood as
other wood finish in the rooms in which it occurs.

Finish. — All standing finish of living-room and dining-room
to be clear, quarter-sawed chestnut. All other standing
wood-work to be clear straight-grained Arkansas or Georgia
pine.

All interior finish to be thoroughly kiln dried. (See painting
specifications for paint and varnishes.) All door and w.mdow
casings, base, etc., in the several rooms to be the style, form and
dimensions as per detailed drawings. All casings, bases, etc.,
to lap well over the ground and fit perfectly to the plastering,
and no finish is to be put up before plastering is thoroughly dry.
Furnish and put up hardwood corner strips, where required, at
all exposed plaster angles, of |X2" to extend 5' 6" above
baseboard, and to have plain square top edges, and to be
scribed on to baseboard at bottom; corners to be slight rounded.
Put up rubber-tipped wood base knobs where necessarv for
doors to swing against, of same wood as finish of rooms. The

196 mechanical drawing.

whole to be done in the most substantial and workmanlike manner
with thoroughly seasoned wood.

All finish to be first clear, except where otherwise specified.

All interior finish must come to the building thoroughly
sanded and ready for the varnish or paint.

Bathroom Toilet Cabinet. — Build toilet cabinet in bathroom
where shown; to be the Hess Warming and Ventilating Co.'s
Sanitary Steel bathroom locker complete (No. 906 Taccma
Bldg., Chicago, 111.), cased up as directed by architect; to have
adjustable and movable enameled steel shelves with rounded
edges, and a plate mirror door. Case to be sunk into wall as
deeply as possible. Height of case from floor to be as directed
by owner.

All interior finish must be absolutely clear and free from
knots and black spots except where painted, which can have
spots or dark streaks, but no loose knots or soft places.

Beam Ceilings.- — All beam ceilings to be as shown on plans
and details.

Mantels. — See details for mantel shelves, bookcases, etc.,
all to be same finish as other finish in rooms in which they occur.
Hearths and face to be Grueby Tile, 6X6", to be selected by
owner or built of face brick, as described in masonry work above
grade.

Hardware. — Contractor is to furnish and put in place all
nails, strap hinges, pulleys, cord and weights for double-hung
windows. All finishing hardware will be furnished by owner
and put on by contractor.

Glass. — The breakage of glass will be evenly divided between
the carpenter, painter, plumber, heating man and plasterer if
party who broke the glass cannot be found. All glass, where

A RCH i TECT URA L D ESIGN .

197

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198 MECHANICAL DRAWING.

not otherwise specified, to be AA double-strength glass, well se-
cured in place.

All glass where marked "Plate" on plans or elevations to be
best American Plate ft" thick and absolutely clear. All mirrors
where shown or described to be ft" plate mirrors, perfectly clear,
and of a size shown or specified. Use metal track and small
wheels in lower rail of sliding doors in pantry and kitchen. All
glass with copper or lead bar muntins to be AA double strength.

Screens. — (Contractor may submit bid screens of his own make,
but use same wire and hardware trimming as hereinafter specified.)

Place Wilier Mfg. Co.'s (Milwaukee, Wis.) or their equal,
patent screens on all double hinge windows and all outside doors.
All screen cloth to be best copper bronzed wire, 16 mesh, and
drawn perfectly tight.

Casement windows to have screens to cover entire window
opening and to be hinged at side to swing in room (see details).
All double-hinge windows to have screens on outside to cover half
of window and to slide up and down on metal springs and wood
strips. Inside screen sash to be constructed of same wood as
finish of rooms in which they occur. All outside screen sash
for windows to be made of same wood as other exterior finish.
Front screen door, No. 151, stiles and rails to be made of quarter-
sawed clear white oak or chestnut, and to be braced with brass
rod and turnbuckle, also to have spring hinge and rubber-ball
bumper. Rear screen door stiles and rails of same wood as other
exterior finish, and to have rubber-ball bumper and brace as above.
All basement windows to have screens to cover entire window,
style No. 3, and to be secured in place by metal thumb turns.

All hardware for screens to be finished by contractor. Use
two 3X3" butts for casement sash; three 4X4" butts for all

ARCHITECTURAL DESIGN.

199

PLATE I.

r7,"nr/ T'f

fl f T.^««l D<vK~ s"

h^s^^i_si ^

Fig. 257.

Residence for G. W. Wilson, Champaign, 111. Brown Brothers, Architects, No. 808-9
Security Savings Bank Bldg., Cedar Rapids, Iowa.

200 MECHANICAL DRAWING.

screen doors; cup catches for all casement screens. All hardware
for screens on outside to be brass. All hardware for screen on
inside of building to be steel, plated to match hardware in room.
Get style of finishes of hardware from the architects.

The contractor must clear out all lumber, shavings, etc.,
and all other loose rubbish from all rooms in the several stories,
sweep all floors clean, and remove all rubbish from the premises
on completion of his contract. All damage to adjoining property
caused by this contractor to be repaired and left clean and whole
on completion.

Tin and Galvanized Iron and Lead Work.

Down Spouts and Conductor Heads. — All down spouts
must be well secured to walls, with ornamental galvanized iron
fasteners, and must extend to ground. Gutters to be made of
No. 26 galvanized iron and properly graded to down spouts.
Provide gutters wherever shown to catch water from the roof,
and provide No. 26 galvanized-iron corrugated down spouts,
3 X 4", where shown on the drawings, or where necessary to carry
the water off the roof to ground. Gutters to run up at least 8"
under shingles.

All valleys to be lined with 20" N. & G. Taylor's Target
and Arrow tin.

Flashings. — Flash around all chimneys, and from roof up into
brickwork, and counterflash same with tin as above specified.
Provide substantial galvanized-iron fasteners for down spouts
where shown. (See details.)

Iron Work. — Provide the Holland Furnace Co.'s (Holland,
Mich.) coal window chute for one coal window in basement.
Also provide all other cast- or wrought-iron work such as ash-pit

ARCHITECTURAL DESIGN.

201

PLATE J.

Fig. 258.

Residence for G. W. Wilson, Champaign, 111. Brown Brothers, Architects, No. 808-9
Security Savings Bank Bldg., Cedar Rapids, Iowa.

202 MECHANICAL DRAWING.

doors, frames, etc., and iron throat and damper for fireplace.
(Covert's Patent Iron Throat and Damper.)

Guarantee. — The whole of the galvanized iron and tin work
must be guaranteed for a term of five years. Provide a tin or
galvanized-iron speaking tube with mouthpieces (one in basement,
one on first floor, and one on second floor where directed). All
to be securely fastened to walls and made perfectly tight.

Painting.

The contractor must find and provide all the necessary ma-
terials of every description, including ladders, scaffolding, ropes,
etc., for the performance of the work in a substantial and workman-
like manner, and of the best qualities of their respective kinds, and
clean off all woodwork before priming it. Putty up all nail
holes, joints, cracks and defects. Sandpaper smooth, and prop-
erly prepare the same before painting the second coat.

Priming. — All outside planed woodwork, such as casings,
sash and frames to be primed as soon as in place with white lead
and linseed oil. All exterior defects in woodwork must receive
a strong coat of shellac before priming. All barge boards, posts,
brackets, etc., to be rough for stain or smooth for paint, as the
owner may direct.

Outside Painting. — Paint all the planed woodwork, two (2)
coats of good white lead or zinc-white and linseed oil, mixed with
colors to bring it to the shade to suit owner. All side wall and
roof shingles, also all rough woodwork, and rough siding if any,
to be given two good brush coats of Cabot's Creosote Shingle
Stain. (Color to suit owner.)

Outside doors, if not of hardwood, to be painted two coats
of zinc white and linseed oil. All outside hardwood doors to be

ARCHITECTURAL DESIGN. 203

stained and then given two coats of Pratt & Lambert's spar
finishing varnish.

All tin and galvanized iron work to be given one coat of min-
eral paint, on under side before laying, then two coats of lead and
oil on finished surface.

Inside Staining, Painting and Varnishing. — All open-grained
woods are to receive one coat of paste wood filler (color to suit
owner) and three coats of Pratt & Lambert's No. 38 preservative
varnish, lightly sanded between coats. Then one coat of Pratt
& Lambert's Dulkote.

All close-grained wood to receive one coat of Pratt & Lambert's
acid stain (color to suit owner). The two coats of Pratt & Lam-
bert's No. 38 preservative varnish lightly sanded between coats.
Then one coat of Pratt & Lambert's Dulkote.

Tinting. — No ceiling or wall tinting in this job.

Floor Finish. — All floors except kitchen and bath to receive
a coat of oil stain to match standing finish and two coats of Pratt
& Lambert's No. 61 floor varnish. Kitchen and bathroom
floors to receive a light oil stain and one coat of white grain
alcohol shellac.

Picture Molding. — The painter is to finish picture mold to
match finish of different rooms and of same materials as specified
for other wood finish in the rooms in which it occurs.

Plumbing.

This specification is meant to embrace all the materials
and labor necessary for a complete system of plumbing, with all
sewers, supplies, wastes and ventilating pipes for the same.
All exposed pipes in rooms to be nickel-plated work, except
where otherwise specified.

204

MECHANICAL DRAWING.

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ARCHITECTURAL DESIGN. 205

Fixtures. — To consist of goods as specified below, and as
shown on the drawings. Numbers all taken from Wolff's "H"
catalogue. (Standard Manufacturing Company's or Mott's goods
will be accepted, where design, size and quality of goods are
the equal of Wolff's as specified.)

Kitchen Sink. — Fig. "H" 8052, to be 18X30". Sink set on
galvanized -iron sink brackets; supply with hot and cold water
through two §" N. P. finished Fuller Compression faucets in
wall over sink, having the "Ideal" centrifugal wastepipe from
wall to soil pipe, and 1" vent pipe to trap.

Bathtub— Wolff's Corona roll rim tub, Fig. "H" 6505,
5' long, first grade enamel finish "Corona," complete, as
described in catalogue.

Laundry Tubs. — Wolff's "W" 8158 complete, as described
in catalogue. Provide wringer holder for these tubs.

Water Closet. — Where shown on plans, put in Wolff's syphon
jet "W" 7085 water closet complete, as shown in catalogue.
Provide the "never-split" seat for water closet. Seat to be cherry
or birch and finished in ivory enamel. Make all necessary con-
nections for supply and waste.

Lavatory. — Furnish and set where shown on plans Wolff's
Fig. "H" 4050, "The Concord," complete, as described in cat-
alogue. Make water connections to all fixtures with the city
mains, and also make proper connections to hot-water pipes
from heater.

Water Heater. — Provide and set in basement where directed
one Ruud automatic gas heater. Make all necessary connec-
tions to water, vent and gas pipes in strict accordance with
printed instructions furnished by the manufacturers, and to
carry hot water to all fixtures except water closet in the

206 MECHANICAL DRAWING.

building. Make proper connection to flue for vent where
directed.

Contractor to make alternate bid on forty-gallon galvanized
iron range boiler in kitchen to connect up with waterback in range
and to all fixtures (except water closet) in the building.

Sewer. — From outside of wall run 4" iron extra heavy soil
pipe under house as directed, to connect to all fixtures in the build-
ing. Continue from outside of house, and run 4" vitrified sewer tile
below front line with cemented joints to cesspool. Sewer to have
an even fall of at least \" per foot, and where branches are made
to different fixtures they must be made with "Y" joints. All
vent, waste and supply pipes to be size and location as per local
city ordinance.

Gas Piping. — Pipe for gas for Ruud heater and to all ceiling
light outlets where shown on the drawings, using f " pipe. All
pipes are to be given the peppermint test, and to be installed
in strict accordance with the local gas company's rules and
regulations.

Waste Pipes. — All waste pipes connecting the different fixtures
to main line of soil pipe are to be of extra heavy lead where they
are not exposed in the room. All exposed work to be nickel-
plated pipes as heretofore specified. All wastes below traps may
be 2" cast-iron soil pipe. Where connections are made to soil
pipes they must be made by means of brass ferrules. Each fixture
is to have a separate trap and is to have a separate vent pipe of
sufficient size run independently through the roof and connected
on main line of soil pipe at a point at least 2' above the highest
fixture in the building.

Water Supply. — The cold water will be taken from city mains
and cistern through f " galvanized iron pipe, and run in as direct

ARCHITECTURAL DESIGN. 207

manner as possible to the different fixtures in the building. Have
a by-pass system of piping.

Hot water to be taken from heater in basement, and run to all
the different fixtures (except water closet) in the building through
§" galvanized iron pipes. All the above supply pipes are to be
galvanized iron, except the traps and connections to fixtures,
which where exposed are to be brass, nickel- plated. Where
iron and lead pipes are connected together it must be done with
brass ferrules. All stop and waste cocks for the proper con-
trolling and draining of these pipes must be provided where directed
by architects. Make openings in walls of house where shown
or directed and supply two sill cocks, Wolff's "H" 561 N. P. J"
with loose key for hose connections as directed.

Water Lift. — Provide and put in place a "Eureka" water
lift in laundry where directed and make proper connections to
city water and cistern for all fixtures.

All the above materials and workmanship to be first-class, put
up by experienced workmen under the immediate supervision
of the plumbing contractor, and when finished to be turned over
to the owner free from leaks, and perfect in every respect. All
to be subject to the acceptance of the local plumbing inspector.
Contractor must furnish certificates of inspection, properly signed,
before owner's final payment will be given.

All cellar floor drains are to be placed where directed and to
comply with city ordinance.

Cesspool (if no sewer). — Where directed by owner build
a brick cesspool 8" in diameter and 10" deep (or as deep
as will be necessary to strike water or sand) with 4" hard-burned
brick walls laid in cement mortar (no brick in bottom). Arch
cesspool over at top and provide a cast-iron ring and cover to be

208 MECHANICAL DRAWING.

2" in diameter and 12" below finished grade. Connect up
to sewer in proper manner and trap the sewer just before
entering cesspool. Contractor to give price ner foot in depth
over 10".

Connect the soil pipe under water closet with 4" standard
cast-iron soil pipe, and continue the same as near as possible
straight up through the roof, having openings and connections to
different fixtures. All joints in soil pipe are to be packed with
oakum, run with molten lead, and thoroughly caulked. No small
vent pipe shall enter the main vent below the highest fixture in
the building.

Electric Wiring.

General Notes.' — No electric work shall be commenced until
all plumbing roughing in is finished. All wiring to conform to
the rules and regulations of the National Board of Fire Under-
writers. All materials used and all work done must be strictly
first class. Contractor must furnish certificates of inspection
properly signed before architect's final certificate will be given.

Wires. — .ALL wires to be carried to the several outlets as shown
on plan, such wires to be of sufficient capacity to carry the number
of lights indicated. All wires must be Habershaw, Okonite or
Roebling white-core, rubber-covered wires. No splicing of wires
will be allowed in the walls.

Switches. — All of the ceiling lights throughout the building,
unless otherwise specified, shall be controlled on Hart Diamond
H. push-button switches, located where shown and having plates
finished to match the hardware of the room in which they occur.
Place switch at top of cellar stairs to control light at foot of stairs
in basement. Place switch on the inside of front door to control

ARCHITECTURAL DESIGN. 209

veranda light. There must be two switches in dining-room,
where shown, to control lights in the center fixture. All of the
bracket lights in the building must be controlled at the fixtures.
See plans for the number and location of lights and all switches.

Outlet Boxes.- — At each outlet place a steel outlet box, pro-
tected with compound to prevent corrosion (ceiling boxes with-
out covers) , and 4J" diameter, all arranged to permit their being
placed over gas-pipe outlet. Where no gas pipe is placed, boxes
to have threaded fixture stubs; outlet boxes to be properly and
firmly secured in position so that outer edge of box or cover will
not project more than \" beyond finished plaster.

Cutout Boxes.- — At point where service enters building place
a fireproof service cabinet; from this service box run one set of
three (3) wire mains to cutout box to be placed where directed.
In service box place a three-pole, single-throw fuse extension
switch connected to mains, and three service wires of sufficient
length to reach street wires, which must be connected to fused end
of switch.

Cutout boxes to be of steel or cast iron set in wall or parti-
tions, and furnished with asbestos-lined paneled door to match
woodwork. In cutout boxes install Edison 3-wire 4-plug cutouts,
with fused plugs complete.

Switches. — Each circuit to be provided with a double-pole
indicating switch. Flush switches to be encased in iron boxes.

Circuits.- — No more than eight lights are to be on any one
circuit.

Capacity of Lights. — Number of light outlets are indicated
on plans. Wires must be heavy enough to carry one 16-candle
power lamp for each outlet.

Bells. — There must be bell in kitchen where directed, to be

2IO MECHANICAL DRAWING.

operated from front door push plate. Place floor receptacle and
extension cord and table push button in dining-room to operate
buzzer in kitchen. Use Sampson or La Clede batteries for all
bells, and guarantee same for one year. All push buttons must
be plated to conform to finish of hardware.

Telephone.' — This contractor must do all interior wiring or
telephone. Said telephone having outlets in rear hall or where
shown on plans.

Heating.

We recommend the Spencer Heater, the Capitol Boilers
and the American Radiator Company's sectional cast-iron
boiler and their cast-iron radiators. Any one of these heaters
will be acceptable. Contractors bidding on this work must
submit a schedule of radiation for each room and give their total
number of feet of radiation to be used in the house. Also fill
out their specification printed blanks complete, giving size of
heater, etc., and submit same to owner along with their bid.

Contractor is to guarantee to heat house to 700 when coldest
weather outside. All basement pipes are to be covered with
asbestos and canvas covering, and all radiators are to be painted
in colors to suit owner.

Brown Brothers, Architects,

No. 808-9 Security Savings Bank Bldg.,

Cedar Rapids, Iowa.

ARCHITECTURAL DESIGN.

PLATE L.

Fig. 263.

212

MECHANICAL DRAWING.

Plate L. Fig. 260 shows the front elevation of a window.
Figs. 261 to 267 give vertical and horizontal sections as indicated
in Fig. 260.

Plate M. Figs. 268 to 273 inclusive, elevations and sections
of gutters.

This plate is to be drawn according to directions given under
" Problems." _

Plate N. Figs. 274 and 275 show a Gothic style of lettering
that is coming into common practice in architectural work
drawings.

These plates are to be made according to directions given
under " Problems."

In finishing the sections of the woodwork, prepare a dark
shade of burnt sienna with a very little Chinese ink added and
draw the wood sections free hand as given in the plate of standard
sections on page 58. Use a Gillott pen No. 303.

ARCHITECTURAL DESIGN.
PLATE M.

213

214

MECHANICAL DRAWING.
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ARCHITECTURAL DESIGN.
PLATE N.

2T5

CHAPTER VIII.
SHEET METAL PATTERN DRAFTING.

Students who have completed Course I in Mechanical Draw-
ing will find little difficulty in understanding the methods employed
in solving the sixteen problems included in the following four
plates of this course.

Prob. i. It is required to make the pattern drawing of the
rectangular box made of sheet tin shown by the isometric drawing
Fig. 276. Fig. 277 shows the elevation and plan in orthographic
projection and Fig. 278 the developed pattern. The J" width
added to the end of the sides are bent double as shown in Fig. 276
and are employed to stiffen the sides. A model of this box may
be seen in the drafting room.

Prob. 2 is a conical piece made in two parts of thin planished
iron. Fig. 279 is an isometrical drawing of the finished piece and
Fig. 280 the orthographic views. Figs. 281 and 282 show the
developed patterns with a TV' allowance on the edges for seams.
See model in the drafting room.

Prob. 3 requires the drawing of a pattern for a flat-sided
tapering box shown in isometric at Fig. 283. Figs. 284 and 285
show the orthographic views and the developed pattern respec-
tively. The seams are to be soldered, therefore an allowance

is not necessary in this case.

216

SHEET METAL PATTERN DRAFTING.

217

218 MECHANICAL DRAWING.

Prob. 4. Make pattern in one piece of the oblong tapering
article shown in isometric at Fig. 286. Fig. 287 gives the ortho-
graphic drawings with dimensions and Fig. 288 the developed
pattern. Divide the small semicircle in the plan into six equal
parts. Draw the two center lines, C and D, in Fig. 224, 2}" apart.
With centers, C and D, and radii r and R draw arcs. From lines,
C and D, step off on the small arc the divisions found on small
semicircle in plan. Through the last division draw radial lines
from C and D and from the latter lay off the remaining side 2J"
long and add $j" allowance to each end as shown.

Prob. 5. Make the pattern drawing of a scale scoop assuming
the two parts of which it is made to be segments of cylinders.
Fig. 289 is the elevation of the scoop with one edge parallel to the
horizontal plane, and the corresponding bottom edge making an
angle of 400 with it.

Having drawn the scoop as given, draw the outline of the
cylinders and at the end of the right hand one, draw a semicircle
equal in diameter to the cylinder and divide the lower quadrant
into six equal parts marking them 1 to 7. Through these points,
1, 2, 3, 4, etc., draw lines parallel to the axis of the cylinder cutting
the upper edge and middle dividing line of the scoop in points 7, 6,
5, 4, 3, 2, i' and i', 2', 3', etc. respectively.

In laying out the development, Fig. 290, draw from the point
7' a line perpendicular to the line 7^7, and at a convenient distance
from the latter draw the center line 1-1 and on the line f-i in
both directions, lay off the six divisions found on the semicircle.
Through these divisions draw lines parallel to 1-1 and intersect
these with perpendiculars drawn from the corresponding points
of intersection of the scoop.

Prob. 6. Draw patterns of scale scoop whose elevation and

SHEET METAL PATTERN DRAFTING.

219

220 MECHANICAL DRAWING.

end view is shown in Fig. 291. This scoop is similar to that of
Prob. 1 except that it is formed from the segments of cones.
Draw the elevation and end view, divide the half of the end view
as shown and through these divisions draw horizontals to cut the
line CD. Draw the outline of the complete Cone and from the
intersecting points on CD draw elements to the apex of the cone.
With the apex A as center and radius A C draw arc of circle 8-
8 and lay off upon it from the center line A-i in both directions
the divisions 1 to 8 found on the end view.

Where the elements of the cone cut the upper edge of the
scoop, drop perpendiculars to the contour element of the cone,
thus finding the true distance of the points from the apex. With
center A and each of these true lengths as radius draw arcs inter-
secting the corresponding elements in the development. Through
these points draw the outline curve of the pattern.

Prob. 7. Make pattern drawings for a scoop with one end
funnel-shaped, Fig. 292. The other end is made from the seg-
ment of a cone exactly like Prob. 1.

The funnel-shaped end is made from a cone, therefore the
methods used in Probs. 1 and 2 can be applied here without any
further directions.

Prob. 8. Draw pattern of grocer's scoop, Fig. 293. The
body of scoop is cut from a cylindrical form as in Prob. 1. The
methods are clearly shown in the drawing. Fig. 294 is the
pattern of the body.

The handle is made up of two cone frustrums and the con-
struction is similar to that used in Prob. 2. Figs. 295 and 296
are the handle patterns.

The student should be able to lay out these patterns without
any further assistance.

SHEET METAL PATTERN DRAFTING. 221

TRIANGULATION.

Many articles in sheet metal work are of such irregular form
that the methods employed in the preceeding problems cannot
be used. It is therefore necessary under such conditions to obtain
the development by measuring the whole surface part by part by
means of triangles. Fig. 297 will illustrate the method of measur-
ing the surface of an article of irregular form by means of triangles.
If the article is symmetrical about its axis it will only be necessary
to divide a quadrant of the top and bottom each with the same
number of equal parts. Fig. 297 is an isometrical drawing of
the irregular figure shown in Fig. 301. The quadrant 1 — 5 is
divided into four equal parts, top and bottom. Join 1 — i",
2-2", 3-3", 4-4" and 5-5". Also join 1-2', 2-2', 2-3',
3 — 3', 3 — 4' 4 — 4f, 4—5' and 5— 5r. These latter lines are the
projections of the lines 1 — 2", 2 — 2r/, 2—3", $ — $", 3 — 4", 4 — 4",
4— 5", and 5 — 5" and are used as the bases for the triangles laid
out at Fig. 302 to find the true length of the lines joining the points
in the top and bottom quadrants, for example i' — 2', in Fig. 302
is the true length of 1 — 2' on the plan of Fig. 301 ; 2"— 2, Fig. 302,
is the true length of 2' — 2 in plan of Fig. 301, etc.

In laying out the development, Fig. 303, 1 — i' is taken directly
from the elevation, Fig. 301, because it is in its true length being
parallel to the vertical plane. The next step is to take i'— 2 , Fig.
301, as a radius and i', Fig. 303, as center, desrcibe an arc 1'— 2',
then with i'— 2', Fig. 302, as radius and 1, Fig. 303, as center,
describe arc putting arc 1 — 2' in the point 2'. With 1, Fig. 303,
as center and 1 — 2, Fig. 302, as radius describe arc 1 — 2, Fig. 303,
and with 2', Fig. 303, as center and 2"— 2, Fig. 302, as radius
describe arc cutting arc 1 — 2 in the point 2 and so on, determining

222

MECHANICAL DRAWING.

SHEET METAL PATTERN DRAFTING. 223

the remaining points, 3, 4, 5, and 3', 4', 5' ji Fig. 303 ji the same
way. The remaining part of the semi-development 5 — B, Fig.
303, is a duplicate of that already found.

Prob. 9. It is required to make a pattern drawing for the
article of irregular form shown in Fig. 298. Draw the plan and
elevation as given and divide the upper and lower half into the
same number of equal parts. Lay out the triangles, Fig. 299, and
determine the development of the left quarter in the same manner
as described above in reference to Fig. 297.

The right half of Fig. 298 is the half of a truncated cone, so
that the development of that part is quite simple. Produce the line
8 — 8' in the elevation, Fig. 298, to C, the apex of the cone, and
when 5 — 5y, Fig. 300, has been drawn, produce it and layoff upon
it from 5, 5 — C equal to 8 — C in Fig. 298. With C as center and
C — 5' and Cf— 5 as radii describe arcs 5' — 8' and 5 — 8 respec-
tively, and complete the semi-development.

Prob. io. Draw the pattern for the article of irregular form
shown in Fig. 301. Sufficient directions for the solution of this
problem were given in reference to Fig. 297.

Prob. ii. Make the pattern drawing for the coal scuttle shown
in Fig. 304. Draw the elevation and plan as given. Observation
will show that the form of the scuttle from 1 — 5 is part of a cone,
so its development can be easily accomplished. The remaining
portion will be developed by triangulation.

Lay out development as follows: with r and r + a, Fig. 304,
as radii describe arcs 1 — 4 and i'— 5', Fig. 305. On the curve
i' — 5', Fig. 305, lay off the points 2', 3', 4', from the divisions of
the small circle in the plan, Fig. 304. Through these points draw
radial lines from C and make a' b' cf a' e' equal in length to abce
of the elevation, Fig. 304, and thus determine the points 1, 2, 3

224 MECHANICAL DRAWING.

4, 5, Fig. 305. Through the points found draw curve as shown.
To determine points 6 and 7 construct the three triangles shown
in Fig. 306. Then with center 5', Fig. 305, and 5' — 6', Fig. 304,
as radius describe arc and with point 5, Fig. 305, as center and
5" — 6', Fig. 306, as radius describe arc intersecting at 6'. With 5,
Fig. 305, as center and 5 — 6, Fig. 304, as radius describe arc and
with 6', Fig. 305, as center and 6' — 6 as radius describe arc inter-
secting at point 6. With the latter point as center, and 6 — 7
from the plan as radius describe arc, and with 6' as center and
6'— 7' from the plan as radius describe arc. With 6, Fig. 305, as
center and radius 7"— 7', Fig. 306, draw arc intersecting at 7'.
With the latter point as center and f— 7 from the elevation as
radius draw arc intersecting in 7. Complete the development
by joining 6—7 with a straight line and join 5 and 6 with an arc
of a circle with radius equal to 5 — 6. Join 5', 6' and f with an
irregular curve. Develop the pattern for base.

Prob. 12. Draw patterns for bath tub given in plan and
elevations in Fig. 307.

Draw plan, elevation, half-right end elevation and half-left
end elevation in the order named. Draw also a half-lett end
view from plan in first angle projection. The half pattern of the
body may be developed at once by the method of parallel lines.
Divide the left end view of tub i^to 4 equal spaces 1, 2, 3, 4, 5,
and step these distances off on the line ab of the development and
draw through the points parallel lines. From the points 6, 4,
3, 2, 1 of the elevation drop perpendiculars to intersect the cor-
responding lines in the development at 1, 2, 3, 4, 5, add 5, 6, and
complete the half deveolpment of the body. The half development
of the warped surface of the foot can now be obtained in the follow-
ing manner : Divide the quarter circle of the corner in the plan in-

SHEET METAL PATTERN DRAFTING. 225

to 4 equal parts in the points 2', 3', 4', 5', 6', and project these
points to the line i' — 6 of the end view. Project the points 1, 2,
3, 4, 5 to the curved line of the end view. Lay out the triangles
to obtain the true lengths of the measuring lines. The heights
are obtained from the end view at A, the bases from the plan.
The true lengths of the upper edge of the pattern are taken from
the plan while the radii for the respective arcs of the lower edge
must be taken from the outline of the pattern for the body : Thus
the radius 1 — 2, Fig. 309, is taken from 1 — 2, Fig. 308, and so on.
The radius 1 — 2', Fig. 309, is taken from 1 — 2' in (^4), 2 — 2' in
Fig. 309 from 2 — 2 (B), 2 — 3' in Fig. 309 from 2" — 3' in (B) and so
on. The development of the pattern of the head piece is found in
a similar way. The line 1 — 1', Fig. 310, can be taken directly from
1 — 1' in the elevation as it is shown there in its true length. To
find the true lengths of the remaining lines the heights of the
triangles are laid off on the line 1/— 2' from the respective lines
in the plan, for example i'— 2' is equal to 1'— 2 in the plan and
so on. The bases of the triangles are projected from the end
view in 6, 5, 4, 3, 2, 1, and each hypothenuse drawn in order.
The arcs 1 — 2, 2 — 3, etc., and 1'— 2', 2' — $', etc., are taken from
the corresponding distances in the plan. The development
may now be completed by drawing arcs, using each hypothenuse
of the triangles in their proper order as radius.

Prob. 13. Draw the development for a two-piece pipe elbow,
Fig. 311.

Draw the plan and elevation to the dimensions given and
develop the half of one piece by the method shown. The
methods used in finding the developments in this plate are so
clearly shown that the student should not require any detail
directions.

226

MECHANICAL DRAWING.

SHEET METAL PATTERN DRAFTING. 227

Prob. 14. Develop the necessary patterns for a three-piece
elbow. Fig. 312.

Prob. 15. Develop the necessary patterns for a five-piece
elbow. Fig. 313.

Prob. 16. Draw the pattern of a two-piece oblong pipe elbow.
Fig. 3T4.

CHAPTER IX.

ELEMENTARY MACHINE DETAILS, INCLUDING SCREWS, NUTS,
BOLTS, KEYS, COTTERS AND GIBS, COUPLING SPRINGS, ETC.

A Screw is a helical projection or thread formed upon a
cylinder and is the most common device used in mechanical

Fig. 315.

combinations. It is employed in the construction of machinery

for producing pressure contact and transmitting motion. WheD

228

ELEMENTARY MACHINE DETAILS. 22Q

the thread of an external screw is made to fit into the corre-
sponding hollow of an internal screw (Fig. 315) the latter is
termed ts nut.

The Pitch of a Screw-thread is the lineal distance its
nut would advance along the axis in one turn. In a single-
threaded screw the pitch is the distance between the centres
of two consecutive threads measured in the direction of the
axis, in a double-threaded screw it is the distance from
centre to centre of every alternate thread, and in a triple-
threaded screw it is a distance that will embrace three threads.
For screw-fastenings, instead of giving the pitch the number
of threads per inch of screw is given — for example, a bolt
of \" diameter has generally 8 threads per inch; this means
that the bolt has a single thread wound around it 8 times for
every inch of its length.

Right- and Left-handed Screws. — Screws are made
right- and left-handed, of which the right-handed are the
more common and are distinguished by their nuts advancing
along the screws when turned in the direction in which the
hands of a watch revolve. On a drawing the right-handed
screws are distinguished by the threads inclining upwards
towards the right hand when the screws are in a vertical
position, as in Fig. 315. When a nut with a right-handed
thread is shown in section the direction of the threads in the
nut is the opposite to the threads on the screw.

The Nominal Diameter of a Screw is the diameter over
the tops of the threads and is equal to the diameter of the
cylinder upon which the thread is cut. It is the area of the
nominal diameter that is considered when estimating the
shearing strength.

23°

MECHANICAL DRAWING.

The Effective Diameter is the diameter at the bottom
of the thread and is equal to the diameter of the hole in the
nut before its threads are cut. Unless when the bolts are
subjected to a shearing stress, it is the area of the effective
diameter that is considered in estimating their strength.

The Depth of the Thread is the distance measured
perpendicularly to the axis of the screw from the top to the
bottom of the thread.

NOTATION.
d= nominal diameter of bolt;
d=- effective diameter of bolt;
d = depth of thread ;
Sx— total depth of V;
p = pitch of thread ;
n = number of threads per inch.
The Forms of Screw-threads in general use in machine
construction are represented in Figs. 316-320. The V thread
is adopted on all screw-fastenings because of the shearing
strength of the threads and frictional holding power, which
is due to the normal pressure on the thread being inclined
\^..V >J p

Fig. 316.
to the axis of the screw. This normal force N, Fig. 316.
may be resolved into two components, one L parallel to the

ELEMhNTARY MACHINE DETAILS. 231

axis of the screw, and the other R at right angles to it.
L represents the load carried by the thread and R the force
tending to burst the nut ; therefore the greater the angle
of the V the greater will be the normal component or
bursting force, and, the friction being proportional to the
normal force, it will increase with the angle of the V. Of
the forms of V threads shown two (Figs. 316 and 317) are in
common use in the United States for bolts and nuts.

The Sellers or United States Standard, a section of
which is shown in Fig. 316, has been adopted by the U. S.
Government, the Railway Master Mechanics' Association, the
Master Car-builders' Association, and many of the principal
manufactories in this country. The sides of this thread
form an angle of 6o° with each other, and are \ of Sx short of
meeting at a sharp point at the tops and bottoms, which
makes the sides of the thread in length equal to } of the
pitch, and the depth of thread S will be expressed by the
formula

d = £ X p sin 6o° = 0.65/ (i)

The effective diameter will then be

d, = d — 26 =d — i.^p = d — l-^-. . . (2)

n '

The relation between the pitch and the diameter will be ex-
pressed by the formula

p = 0.24 |/V_j_ 0.625 -0.175. . . . (3)
The number of threads per inch is

n = - = — . . . (4)

p 0.24 s/d + 0.625 -0.175

232

MECHANICAL DRAWING.

The table of proportions on page 70 has been deduced from
the preceding formulae. A difference, however, may be found
between the formulae and the table in the number of threads
per inch, as the table has been modified to avoid as far as
practicable troublesome combinations in the gears of screw-
cutting machines.

Exercise 1. — Draw 6 threads in sectional outline, of the
Sellers thread (Fig. 316), suitable for a screw 6" in diameter.
Scale three times full size.

Construction. — Begin by drawing a horizontal line in the
upper left-hand corner of the paper £■" down from the border-
line, and a vertical line about f " in from the left-hand border-
line. Then find the pitch p by the formula (3), and from
where the two lines you have just drawn intersect mark off
with the scale on the horizontal line 6 points a distance
apart equal to the pitch as found by the formula. Through
these points with the 300 triangle draw the Vs. Complete
the pencilling by dividing the depth of the V into 8 equal
divisions, and cut off one division at the top and bottom of
each thread.

The Sharp V Thread, shown in Fig. 317, is one of the

\ — p—A

Fig. 317.
forms of threads that were in use before the Sellers thread

ELEMENTARY MACHINE DETAILS. 233

was adopted as the U. S. standard, and is still used, although
condemned by all progressive engineers. This thread is the
■same as the Sellers thread except that the sides are made to
meet at a sharp point at the top and bottom, which makes
the sides of the thread equal in length to the pitch/, and
the depth of the thread 8X will be expressed by the formula

6X = / sin 6o° = 0.866/ (5)

The effective diameter of the bolt (d}) will then be expressed
by the formula

dx = d — 2 X o.866>= d— 1.732. . . (6)

Now, comparing the effective diameters, we have:

U. S. threads dl = d — i.$p (2)

V threads ^ = ^—1.732/ (6)

This serves to show that with an equal pitch the effective
diameter of the screw having a U. S. standard thread is
greater than one with a sharp V thread. While the latter form
of thread materially diminishes the strength of the bolt, the
sharp point adds very little strength to the thread. A fur-
ther objection to this form of thread is the variation in depth
of the threads due to the wear of the sharp points on the taps
and dies used in producing them.

The Whitworth V Thread, an outline section of which
is shown in Fig. 318, is the British standard, and is generally
adopted on all screw-fastenings in British machine construc-
tion. It has the sides of the V inclined to each other at an
angle of 550, and has an amount rounded off at the top and
bottom equal to \ of the total depth of the V. The table oj

234

MECHANICAL DRAWING.

dimensions for Whitworth screws (page 70) has been deduced
from the following formulae. The total depth of the V

di== 0.5 cot 27i° = 0.96/ (7)

Fig. 318.

The depth of the finished thread

S = I X 0.96/ = 0.64? (8)

The pitch / = o.oZd +0.04 (9)

Number of threads per inch

1 , I

= — and p = —

p r n

(10)

The diameter at the bottom of the thread will be given by
the formula

1.28

</,=^-2X O.64/ = d —

(II)

Exercise 2. — Draw 6 threads of the Whitworth form of
thread (Fig. 318). Pitchy. Scale three times full size.

Construction. — At a suitable distance below the drawing
of the Sellers thread draw two horizontal lines parallel to
each other and a distance apart equal to 0.96/. On the
upper line mark off a distance ab equal to the pitch. Bisect

ELEMENTARY MACHINE DETAILS. 235

ab and draw the bisecting line to cut the lower parallel line
at the point c. Join ca and cb, which will be inclined to each
other at an angle of 550. Mark off the pitch from b along
the upper line, and from c along the lower line, to give the
required number of threads. Complete the pencilling by
rounding off the sharp points of the V.

The Square Screw-thread. — The form of thread which
is invariably called the square thread is really a rectangle,
the depth of the thread being equal to 0.485/ and its width
equal to 0.5/. However, it is usual and accurate enough
to make it square upon the drawing. * On screws of the
same diameter the pitch of a square-threaded screw is usually
made equal to twice the pitch of one with a V thread ;
therefore the square thread will have only half the amount
of material at the bottom of the thread that the V thread
has to resist the shearing action of the load. As the bearing-
surfaces of this screw are perpendicular to the axis, and the
force applied parallel to it, there will be no bursting force
upon the nut ; and as the reaction is nearly equal to the load
on the square-threaded screw, there will be less friction than
there is under the same conditions with a V thread; conse-
quently the square thread is best adapted for transmitting
motion when the load has to be moved in opposite directions.

The Knuckle or Rounded Screw-thread is a modifica-
tion of the square thread in which the top and bottom of each
thread are made semicircular, as shown in Fig. 379. This form
of thread is used for rough work and can be readily thrown
in and out of gear with a portion of a nut.

The Buttress Screw-thread is a combination of the V
and square threads, one side being perpendicular, and the

♦Klein gives />=.o8-f .09^, dx = .gid— .08.

236

MECHANICAL DRAWING.

other inclined at an angle of 45 ° to the axis of the screw,
&nd has an amount cut from the top and bottom of each

Fig. 319.

thread equal to ■§• of the total depth of the thread, as shown
in Fig. 320. This form of thread can be used only when the
pressure is on that side of the thread which is at right angles
to the axis of the screw.

Fig. 320.

Exercise 3. — Draw the sectional outline of the square,
knuckle, and buttress threads shown in Figs. 319 and 320.
Pitch 1". Scale twice full size.

Pipe-threads Previous to the year 1862 no common

system had been agreed upon for the form or proportions
of pipe-threads. Since that time, owing to the efforts of
the late Robert Briggs, C.E., who proposed formulae and
tables for the dimensions of pipes and pipe-threads, a standard

ELEMENTARY MACHINE DETAILS.

237

TABLE 1.
STANDARD DIMENSIONS OF WROUGHT-IRON WELDED TUBES.

(Briggs Standard.)

Diameter of Tube.

Screwed Ends.

Thickness

Nominal
Inside.

Actual
Inside.

Actual
Outside.

Metal.

Number of

Threads per

Inch.

Length of
Perfect
Screw.

Inches

Inches.

Inch.

No.

Inches.

O.270

O.405

O.068

O.19

O.364

O.540

O.088

O.29

O.494

O.675

O.091

O.30

O.623

O.840

O.IO9

0.39

O.824

I.050

0.II3

O.40

I.O48

I-3I5

O.134

II*

0.51

I.380

I.660

O.140

0.54

1. 6lO

I.900

O.I45

0.55

2.067

2.375

O.I54

II*

O.58

2.468

2.875

O.204

O.89

3-067

3.500

O.217

0.95

3.548

4.000

0.226

I. OO

4.026

4- 5oo

O.237

I.05

4-508

5.000

O.246

I. IO

5-045

5.563

O.259

I.l6

6.065

6.625

O.280

I.26

7-023

7.625

O.301

I.36

7.982

8.625

O.322

I.46

9.000

9-625

0.344

i-57

10.019

10.750

O.366

1.68

Taper of conical tube-ends, 1 in 32 to axis of tube (f in. per foot total taper),

system has been generally used and was formally adopted by
the manufacturers of wrought-iron pipes and boiler-tubes and
by the Association of Manufacturers of Brass and Iron Steam-,
Gas-, and Water-work of the United States.

The following is an extract from a paper by Mr. Briggs
as given in the report of the American Society of Engineers:

11 The thread employed has an angle of 6o° ; it is slightly
rounded off, both at the top and at the bottom, so that the
height or depth of the thread, instead of being exactly equal
to the pitch, is only four fifths of the pitch, or equal to 0.8—,

238

MECHANICAL DRAWING.

if n be the number of threads per inch. For the length
of tube-end throughout which the screw-thread continues
perfect the empirical formula used is T— (o.8Z> + 4.8) X-
where D is the actual external diameter of the tube through-
out its parallel length, and is expressed in inches. Further
back, beyond the perfect threads, come two having the same
taper at the bottom, but imperfect at the top. The remain-
ing imperfect portion of the screw-thread, furthest back from
the extremity of the tube, is not essential in any way to this
system of joint ; and its imperfection is simply incidental to
the process of cutting the thread at a single operation.

Exercise 4. — Draw a section of a pipe-screw (Fig. 321) for
a wrought-iron pipe 8" in diameter. Scale five times full size.

L ^ THffEADS _Ji_2THflrAPS± Comblftf Thbitao

V^^/MP£RrECT ^FUUA.TRO<$ LOHPLCTC IHBCAO

U 4p *L — ip — X T —

Fig. 321.

Construction. — Draw two lines parallel to each other at
a distance apart equal to the thickness of metal as given in
the table ; then draw the vertical line 2 to represent the end
of the pipe, and from 2 along the line I mark off 3, 4, equal
to T. Taper 1 in 32 means an inclination of 1 unit in height
to every j 2 units in length. From the point 4 draw the line 5
at the required inclination. On the line 5 from where it
intersects 2 mark off points at a distance apart equal to the
pitch, and through these points with the 300 triangle draw the

ELEMENTARY MACHINE DETAILS.

239

threads. The bottoms of the last 4 threads are cut off by
drawing a line from the bottom of the last thread that is
full at the bottom to a point on the surface of the pipe which
is a distance beyond the screwed part equal to the pitch.

Screw-thread Conventions. — The method of drawing
screws to represent their true form is shown in Fig. 315,
but it is quite obvious that it is unnecessary for the drafts-
man to perform this lengthy geometrical construction to
indicate each screwed piece upon the drawing. Instead
he adopts some convention suitable to the class of draw-
ing he is making that can be quickly drawn and is generally
understood to represent a screw-thread. Fig. 322, No. I,

shows a convention for a double V thread; No. 2, a single
V thread; No. 3, a single square thread; No. 4, a single
left-hand V thread; No. 5, a double right-hand square
thread; No. 6, any V thread of small diameter; No. 7,
any thread of very small diameter. The method adopted
on rough drawings and sketches is shown at No. 7. The
dotted lines indicate the bottom of the thread, and the
distance they extend along the piece the length of the

240

MECHANICAL DRAWING.

screwed part. At Nos. I, 2, 4 are shown conventions
adopted upon finished drawings to represent threaded screws
of a large diameter and wide pitch. There are various ways
of improving the appearance of this convention : one is
by shading the lower lines of each thread, as shown in Fig.
324; and another method is to fill in completely the
under side of the thread. At No. 6 is shown a method
adopted on working drawings to represent screw-threads
upon pieces of a small diameter or large screws drawn
to a small scale. Here the narrow lines indicate the
top and the wide lines the bottom of the screw-thread.
When a very long screw has to be represented upon a draw-
ing, as is often the case with the square-threaded screw, a
few threads are drawn at the beginning of the screwed part,
and the length of the screw is indicated by dotted lines drawn
from the bottoms of the threads.

The Nut. — The most common application of the screw
for producing contact pressure is the bolt, used in conjunction
with a nut, of which there are different forms. The form
most in use is the hexagonal (Fig. 324).

The standard proportions for hexagonal nuts are :

H= height = diameter of bolt (d).

F = distance across the flats = i\d -\- \ of an inch.

D = distance across the corners = (\\d-\- -J-") 1.155.

Fig. 323 shows the true form of the curves when the end
of the nut is machined to form a part of a sphere or cone.
This rounding or bevelling off of the corners is called cham-
fering. The radius r of the chamfering is made from i^d to
2dy and the angle a is made from 6o° to 45 ° with the axis of
the nut. When representing nuts upon a drawing they should

ELEMENTARY MACHINE DETAILS.

241

always be drawn to show the distance across the angles, as in the
elevation Fig. 323.

Exercise 5. — Draw the true curves of a hexagonal nut for
a bolt 6" in diameter when the top of the nut is chamfered

Fig. 323.
off to form a part of a sphere with a radius r = I J times the
diameter of the bolt (d), and when the chamfering is a part

242 MECHANICAL DRAWING.

of a cone the side of which makes an angle of 450 with the
axis of the nut, as shown in Fig. 323.

Construction. — Begin with the plan, first locating the cen-
tre c, and with f as a centre and a radius equal to \d draw
the quadrant representing the hole in the nut, and from the
same centre and a radius equal to half the distance across the
flats F draw the quadrant Q, and on this quadrant circum-
scribe a part of a hexagon with the 300 triangle and T square,
as shown in Fig. 324. Draw the part elevations and end
views, and with r as a radius and the centre on the centre
line draw the arc 5, which represents the spherical chamfer,
and on the lower elevation draw the angle a. Divide eb into
any number of divisions, say 6, at points 1, 2, 3, 4, $d.
Where perpendicular lines drawn through these points intersect
the arc 5 and line L draw the horizontal lines 7, 8, 9, 10, 11,
12, 13, and with c as a centre and radii ci, c2, c$, C4, c$
draw arcs, and from where these arcs intersect the inclined
face of the nut draw vertical lines to intersect the lines 7, 8,
9, 10, etc. These points of intersection will be points of the
curve on the side face of the nut. The curve of the front
face will be an arc of a circle. To find the curves on the side
view draw a line 15 say \" below and parallel to the lower
face of the nut in plan, and a perpendicular line 14 half
an inch to the left of the end view; where the arcs drawn
through the points 1, 2, 3, etc., from the centre c cut the
inclined face of the nut in plan draw horizontal lines to inter-
sect the line 14 ; and with a centre at the intersection of the
lines 14 and 15 revolve the lines 17, 18, 19, 20, 21, 22, 23
on to the line 15 and draw perpendicular lines through the
points of intersection. The line 17 revolved will be the cert-

ELEMENTARY MACHINE DETAILS.

tre of the nut face on the end view, and the intersection of
the lines 17, 18, 19, 20, 2 1, 22, 23 with the horizontal lines
7, 8, 9, 10, 11, 12, 13 will be points on one half of the re-
quired curve. To complete the curve, with a centre at the
intersection of the line 17 and the top of the nut mark with
the compasses corresponding points on the other side of the
line 17.

Fig. 324.

A Conventional Method of representing large nuts on
drawings is shown in Fig. 324. In this representation the
curves of the nut are arcs of circles and the corners are
chamfered off at an angle of 45 ° to the axis of the nut,

244

MECHANICAL DRAWING.

TABLE

UNITED STATES STANDARD OF

Screw-threads.

Diameter

Screw.

Number

of
Threads
per Inch.

Diameter

Bottom

Threads.

\rea at

Bottom

Threads in

Square Inches.

Area of

Bolt Body

Square Inches.

%
5/16

7/16

%
9/16

20
18
16
14
13
12
II
10

.185
.240
.294

•344
.400

•454
.507
.620

•73i

.027

•045
.068

•093
.126
.162
.202
.302
.420

.049
.077
.IIO
.150
.196
-249
•307
•442
.601

.837
.940
1.065
1. 160
1.284
1.389
1. 491
1. 616

•550

•694

.893

I.057

1.295
I. 515
I.746
2.051

.785
•994
1.227
1.485
1.767
2.074
2.405
2.761

2
2%

4K
4K
4
4

1. 712
1.962
2.176
2.426

2.302
3.023

3-719
4.620

3.142
3.976
4.909
5 -940

3X
3

2.629
2.879
3.100

3-317

5-428
6.510
7.548
8.641

7.069

8.296

9.621

11.045

2^
2#

3-567
3.798
4.028
4.256

9-963
II.329
12-753
14.226

12.566
14.186
15.904
17.721

2^
2^
2^
2^8
2X

4.480
4.730
4-953
5-203

5.423

I5.763
17.572
19.267
21.262
23.098

I9-635
21.648
23.758
25.967
28.274

Note.— The above table gives the sizes of the rough nuts and bolt-heads. The finished

ELEMENTARY MACHINE DETAILS.

245

SCREW-THREADS, BOLTS, AND NUTS.

Nuts.

Heads.

Tap Drill.

h"^ — 1

M, \

|>U

yw/s/s.

(Xil)

to;

CZJ

37/64

7/10

3/l6

5/16

19/32

11/16

10/12

5/16

19/64

u/16

51/64

63/64

n/32

5/16

7/16

25/32

9/10

7/16

25/64

23/64

7/16

13/32

9/16

31/32

ill

9/16

31/64

15/32

T 7

1*5

17/32

'If

T49

T 7

rT5

Ifi

2^V

23/32

lj&

»H

13/16

27/32

III

29/32

31/32

»A

2|f

T 3

X1TS

0 3

2lff

3/*

irt

T 8
T37

3ll

/,31

T 9
I37

3tV

3ff

i]4

o 1 5

3*1

i*l

3X 3^

iy9w

4tV

4li

1F?

2/2

5fi

ill

*ft

4|f

2TV

3 ,

5y|

7tV

2/2

«8I

z32~

71!

6fi

8ft

3tV

335

7t\

3Tf

7fi

3tV

CI 3
°S2

10X

027

lot!

9a*

TT2S

9ff

11^

4fV

4fi

10A

I2#

43A

«>H

,,16

I2rs

H=d-x/xV'\ F= iid + 1/16": A=4-i/i6"; A, =

ri^+i/16'

246

MECHA NIC A L DRA WING.

The A. L. A. M. Standard Screws and Nuts.— The

form of the screw thread is the U. S. Standard as shown in
Fig. 316. The number of threads per inch for the A. L. A. M.
bolts and nuts is given in Table 3. Bolts and nuts are
made of steel, whose tensile strength must not be less than
100,000 pounds per square inch and elastic limit not less
than 60,000 pounds per square inch.

TABLE 3.

A. L. A. M. STANDARD SCREWS AND NUTS.

Number of
Threads.

0 i

ift

The length of the threaded portion of the bolt should be about
1 \ times the diameter.

Bolt heads and plain nuts are flat chamfered, as in Fig.

324.

Castle nuts have a spherical chamfer, as in Fig. 324.

Bolts and nuts are finished with what is known as screw
makers' " semi-finish."

Screws, screw heads, and plain nuts are left soft, while castle
nuts are case-hardened.

ELEMENTARY MACHINE DETAILS.

24!

The body diameter of the screw is one-thousandth of an inch
(.001) less than the nominal diameter. The clearance between
top and bottom of threads in nuts is correct when the top
is made from two-thousandths to three-thousandths of an
inch large.

Nuts are made to fit without apparent shake. Fig. 325 shows
the A. L. A. M. bolt and castle nut. The facing under the head

{ 1 *

$.b ~W*(

[ 1 jL

and nut is made equal in diameter to the distance across the
flats and is made so that the scratching of the nut when it is being
screwed on to a finished surface will not show. It also increases
the pressure per square inch.

Split Pins, when made of a uniform diameter from wire
of a semicircular cross-section and provided with a head,
as in Fig. 326, are used for preventing pieces from sepa-
rating, while allowing a slight motion in the direction of
the axis of the piece that they pass through. The method
of drawing split pins is clearly shown in Fig. 326. The diam-
eter of the pin, in proportion to the diameter d of the piece
it passes through, may be = .05^ + .13, taking the nearest
size in jfe".

248

MECHANICAL DRAWING.

Taper Pins, shown in Fig. 327, are used for securing one
piece to another in a fixed position. They are sometimes

Fig. 326.

split at the small end, and opened out in the same manner
as the ordinary split pin, to prevent slacking back. The
diameter of the tapered pin at the large end, in proportion

Fig. 327.

to the diameter (d) of the piece through which it passes, may
be made = .o6d + .13 and taking the nearest size from Table 4
(page 249).

Keys are employed to connect wheels, cranks, cams,
etc., to shafting transmitting motion by rotation. They are
generally made of wrought iron or steel, and are commonly

ELEMENTARY MACHINE DETAILS.

249

TABLE 4.

STANDARD STEEL TAPER-PINS.

Taper one-quarter inch to the foot.

dumber

Diameter at {
larye end |

.i*

.17.

•193

.219

.250

.2S9

•34i

.409'. 492

•59i

.706

Approximate )

fractional V

sizes )

5/32

II/64

3/16

7/32

19/64

11/32

13/32

19/32

23/32

Longest limit \_
of length )

l/z

rectangular, square, or round in cross-section. The form of
key in general use is made slightly tapered and fits accurately
into the key-way, offering a frictional holding power against
the keyed piece moving along the shaft. The groove or part
where the key fits on the shaft, and the groove into which it
fits on the piece it is holding is called the key-bed, key-
way or key-seat. For square or rectangular keys, when the
keyed piece is stationary on the shaft, the bottom of the
groove on the shaft is parallel to the axis, while that of the
groove in the piece it is securing is deeper at the one end
than the other to accommodate the taper of the key.

Keys may be divided into three classes: 1. Concave or
saddle key; 2. flat key; 3. sunk key.

Saddle Key. — This form of key has parallel sides, but is
slightly tapered in thickness and is concaved on the under
side to suit the shaft, as shown in Fig. 328. As the holding
power depends entirely upon the frictional resistance, due to
the pressure of the key on the shaft, the saddle key is only

250

MECHANICAL DRAWING.

adapted for securing pieces subjected to a light strain. When
this key is used for securing a piece permanently, the taper is
usually made 1 in 96, but when employed on a piece requir-
ing to be adjusted, such as an eccentric, the taper is increased
to I in 64 to allow the key to be more easily loosened.

Fig. 328.

329

Flat Key. — This form of key, Fig. 329, differs from the
saddle key in that it rests on a flat surface filed upon the
shaft. It makes a fairly efficient fastening, but as it drives
by resisting the turning of the shaft under it, there is a tend-
ency to burst the keyed-on piece.

TABLE 5.

DIMENSIONS OF SADDLE AND FLAT KEYS.

iy2

5/16

3/8

7/16

3/16

5/16

7/16

9/16

Sunk Keys are so called because they are sunk into the
shaft and the keyed-on piece, Fig. 330, which entirely pre-
vents slipping. For engine construction they are usually
rectangular in cross-section and made to fit the key-seat on
all sides. When subjected to strains suddenly applied, and

ELEMENTARY MACHINE DETAILS.

251

Fig. 331.

in one direction, they are placed to drive as a strutj
diagonally, as in Fig. 331.

Fig. 330.

Fig. 332.

The following table, taken from Richards's " Machine
Construction," agrees approximately with average practice:

TABLE 6.

DIMENSIONS OF RECTANGULAR SUNK KEYS.

3 3'A

5/16

7/16

S/8

% %

1/8

ifg

T 5/32

3/16

9/32

5/16

7/16 %

n/16

13/16

In mill-work, for fastening pulleys, gear-wheels, coup-
lings, etc., to shafting they are made slightly greater in depth

252

MECHANICAL DRAWING.

than breadth. For machine tools they are generally square

in cross-section. The following table gives the sizes of keys

used by Wm. Sellers & Co. both for shafting and machine

tools:

TABLE 7.

3^
11/16

„

5/i6

5/16

7/16

7/i6

9/16

11/16

n/16

11/16

„

D
B
T

13/16

aA
13/16

5
13/16

slA

15/16

I5/I6

7
1^

VA
1^

8
1^

Round Keys. — Taper-pins (Fig. 332) are sometimes used
as keys to prevent rotation where a crank or wheel is shrunk
on to the end of a shaft or axle. Round keys are used in
such a case because of the ease in forming the key-way,
which is simply a tapered round hole drilled half into the
shaft and half into the shrunk-on piece. The standard pro-
portions of the pins are given on page 249. The size at the
large end nearest to £ of the shaft diameter may be used for
this purpose.

Fixed Keys are used when it is undesirable to cut a long
key-way on the shaft to allow the key to be driven into place
after the keyed-on piece is in position. The fixed key is
sunk into the shaft, as in Fig. 333, and the keyed-on piece is
driven into position after the key is in place.

When a keyed-on piece has to be adjusted to different
positions on the shaft, to avoid the trouble of drawing a
tight key in and out, it is made to slide in the key-way, and
the keyed-on piece is held against moving along the shaft by
means of set-screws, as shown in Fig. 334-

ELEMENTARY MACHINE DETAILS.

253

Fig. 333. Fig. 334.

Sliding Feather Key. — This system of keying secures
the piece to the shaft, to transmit motion of rotation, and at
the same time allows the keyed-on piece to move along the

Fig. 335. Fig. 336.

shaft. They may be secured to the keyed piece and slide in
a groove on the shaft, as in Fig. 335, or secured to the shaft
and slide in the groove in the keyed piece, as in Fig. 333.
The dimensions for this form of key may be taken from
Table 7.

Woodruff Keys.— This system of keying (Fig. 337) is
used for machine tools, or wherever accurate work is of first
importance. With this form of key, as the key rights itself
to the groove in the keyed-on piece, there is no danger of

254

MECHANICAL DRAWING.

the work being thrown out of true by badly fitted keys, and,
being deep in the shaft, it cannot turn in the key seat

No.

1 n

5 //
64

A'-

it"

7 /.'
64

Tor if"

i" or if"

*" or if"

i|"

ii" or i&'

if" or i A'

No.

ii"

iy toif"

If"

1 ■•/

lA'toif

I*"

itt"toir

I*"

7 //

itt" to if"

I*"

7 /•
64

lif" tO 2\"

2*"

2" to 2f"

Ii'

3 /'

7 //
64

2" tO 2\"

&\-

Fig. 338.

The "Woodruff " key, reaching deeper into the shaft than one
of ordinary construction, is more firmly imbedded, and hence
capable of standing a much greater strain.

It is impossible for a Woodruff key to roll over in its seat, as is

ELEMENTARY MACHINE DETAILS.

255

often the case with an ordinary key. In case of an accident,
Woodruff keys have been known to shear off without damaging
pulley or shaft, where an ordinary key of the same width would
roll in the seat and destroy both pulley and shaft. Whitney
Manufacturing Company.

COTTERS

are keys employed to connect pieces which are subjected to
tensile and compressive forces. They are driven transversely

Fig. 339.

through one or both of the connected pieces and transmit power
by a resistance to shearing at two cross-sections. The cotters
are usually made rectangular in cross-section, and the ends
rounded, as shown in Fig. 339.

256 MECHANICAL DRAWING.

The cotter-way with the rounding ends is generally
adopted, as it is easier to make, which is done by drilling two
holes of a diameter equal to the thickness of the cotter and
cutting out the metal between them. Again, this form of
cotter-way does not weaken the cottered pieces to quite the
same extent as when the corners are left sharp. The cotters,
however, are not so easily fitted into cotter-ways with round
ends, and for that reason some engineers make the cotters of
rectangular cross-section, fitted into corresponding cotter^
ways.

Taper of Cotters. — When cotters are employed as a
means of adjusting the length of the connected pieces, or for
drawing them together, they are made tapered in width, as in
Fig. 339, but when used as a holding-piece only, the side? are
parallel. When tapered cotters depend upon the friction
between their bearing-surfaces for retaining them in position
the taper should not be more than 1 in 24 (J" per foot), but
where special means are employed for holding the cotter
against slacking, the taper may be made as great as 1 in 6
(2" per foot).

Forms and Proportions of Cotter-joints. — When the
fastening is subjected to tension only, the arrangement shown
in Fig. 339 is used for securing two pieces together by means
of a cotter. Fig. 339 shows a method of fastening two
rods, R and R\ together to resist thrust and tension. The
joint is made by fitting the end of the rod R into a socket 5
formed on the end of the rod R ' ', and through the socket and
rod end driving a cotter until the collar C bears against the
socket end. \

ELEMENTARY MACHINE DETAILS. 257

As a cotter-joint is proportioned to withstand the greatest
longitudinal force transmitted by the rod, all parts will there-
fore be proportional to the diameter dx of the rod, unless
where the dimensions of the rod are increased to insure stiff-
ness. The following proportions are in accordance with good
practice:

b, breadth of cotter = 1.3^;

/, thickness of cotter = .3^,;

d> diameter of pierced rod = \.2dx\

D, diameter of socket in front of cotter == 2.4^ or 2d.

Dx, diameter of socket behind cotter = 2dx\

Dti diameter of collar on rod R = 1.5^,;

/, thickness of collar on rod R — \dx;

/, the length of the rod and socket beyond the cotter = from

\dx to dx.

VVhen d is known the diameter of the solid rod (d\) = .82^.
The clearance c may be made \". The cotter need not extend
beyond the greatest diameter of the socket more than \" when
driven home.

COTTER AND GIB.

When one of the pieces connected by the cotter is
a thin strap, as in Fig. 340, a second cotter, called a
gib, is used. The gib is provided with a head at the
ends which project over the strap S, thus preventing it
(the strap) from being forced open by the friction between it

2S<

MECHANICAL DRAWING.

and the cotter as the latter is driven into place. Figs. 340
and 341 show the application of gib and cotter to strap-end
connecting-rods, where R is the rod and S the strap. When
two gibs are used, as . in Fig. 342, the sliding surface on each
side of the cotter is the same. Instead of having both gibs
tapered, as shown in Fig. 342, one of them may be parallel
and the taper all on one side of the cotter. The strength of
the gib and cotter in combination is made the same as the

Fig. 34c.

Fig. 341.

Fig. 342.

single cotter and should be proportional to the strap 5. The
working strength of the strap at the thinnest part is found by
the equation

2BTft = P.

from which

T =

2Bft

(12)

where Pis the maximum pull on the xo\ T the thickness,

ELEMENTARY MACHINE DETAILS.

259

and B the breadth of the strap. Then as the gib and cotter
are to have the same strength as the single cotter, and as B is
equal to, or a little greater than d (the diameter of the rod), t
may be made equal to .25$ and

I2BT
V.7854

T', the thickness of the strap where it is pierced by the cotter,
should not be less than 1.3 7\ V, the distance from the gib to
the end of the strap, = 2 J1. /, the distance from the cotter to
the end of the rod, = 1.5^ c, the clearance, should not be less
than cf (the difference between the widest part of the eotter and
the width of the cotter at the top of the gib-head). The method
of constructing gib-heads is shown in Fig. 341, where h, the height
of the gib-head, = 1 \t.

Nut Wrench. — Fig. 343 shows a common straight nut

wrench. They are made of wrought iron or steel, drop forged.
Table 9 gives the usual proportions.

260

MECHANICAL DRAWING.

TABLE 9.

PROPORTIONS FOR WRENCHES.

B = WX.&

D = WX.6$

F=WX.2S

L = WX.7

Fig. 344.

Helical Springs. — The following formulae is given by
Clarke, who quotes from a report on safety valves made by
the Inst, of Engrs. and Shipbuilders of Scotland:

d3Xw Iwd

E = KTt:^ D = x — , for round steel.

and

D = ^l — , for square steel.
4-9

E = compression or extension of one coil in inches;

d= diameter from center to center of steel bar of which the

spring is made, in inches;
w = weight applied in pounds;

D = diameter, or side of the square of the steel bar, in six-
teenths of an inch;
C=a constant, which may be taken as 22 for round steel
and 30 for square steel.

To obtain the total deflection for a given spring, multiply the
deflection for one coil by the number of free coils.

ELEMENTARY MACHINE DETAILS.

261

In Fig. 344, 4 is an example of a helical tension spring and 5
that of a compression spring.

Fig. 345.

Fig. 345 shows an example of a coil spring for a steam safety-
valve with its spindle.

Cast-iron Flanges. — Figs. 346 and 347 show drawings of
cast iron flanges of ordinary design. Their correct proportions
are given in Table 10.

Fig. 346.

Fig. 347.

Chains. — Fig. 348 shows a drawing of a common end link
and narrow shackle used for general purposes. Table 11 gives
the United States Navy standard proportions.

262

MECHANICAL DRAWING.

TABLE 10.

PROPORTIONS FOR FLANGES.

Dia.

Bolt.

1
4

7
8

IOj

1.3

: 8

Fig. 348.

TABLE 11.

C
6*

F
2^

1
4

L
4i

N
5

n
I

2lV

■6*

3t16

3+*

3tt

7
T6

ELEMENTARY MACHINE DETAILS.

263

Ball Crank Handle. — Fig. 349 shows a drawing of a form
of handle used for ball cranks on machine tools. The dimensions
are given below in Table 12.

HGK-£3

Fig. 349.

o 1

-C7

*pZZZ23ZBL

Fig. 350.

W/M///A

TABLE 12.

No.

1
4

_5_

n3*

§i

1 A

Washers. — Fig. 350 is a cross-section of the ordinary circular
washer for all kinds of bolts. Table 13 gives the proportions
for different diameters of bolts.

TABLE 13.

Diam. of

u. s.

Diam. of

U. S.

Bolt.

Wire Gauge

Bolt.

Wire Gauge

No. 18

No. 9

No. 16

No. 9

No. 16

No. 9

No. 14

No. 9

No. 14

No. 8

No. 12

No. 8

No. 12

No. 8

No. 10

No. 8

No. 10

No. 8

264

MECHANICAL DRAWING.

Fig. 351.

CRANE HOOKS.

Notation: *

P = load in pounds;
A = area in square inches;
R2 = square of the radius of gyration;
/= allowable fiber strain in pounds per square inch.

P Pxex_P Pxei
J~~A ~T~~ A AR2'

1 +

xe\
R2

. . . (General Formula)

* American Machinist, Oct. 31, 1901.

ELEMENTARY MACHINE DETAILS.

For section considered as a trapezoid

AJ-±^Xd, . . (I) R2_dW + 4bc + c>)

b + 2C d

(3)

X =

b + 2c d\

Assuming b =.656^; c = .2id. Then
P d3

f 7. 79^+11. n^r'
D = 2r+i%d, di = o.$d.

26;

(2)
(4)

(5)

Flc 35-

P and / being known, assume r to suit. Divide P by / and
.find the quotient in the column headed by the required r, in

266

MECHANICAL DRAWING.

Table 14. At the side of the table in the same row will be found
the necessary depth of section d.

TABLE 14.

.50

.75

1 .00

1. 25

1 -SO

1. 75

2 .00

2.25

2 .50

2.75

3 .00

2.00

.378

•335

.300

.271

.248

.228

.212

.197

.184

•173

.164

2.25

-493

.440

•397

.362

•333

.308

.286

.267

.251

.237

.224

2.50

.624

.562

.511

.468

• A32

.401

•375

-352

-330

.312

.296

2.75

.771

.698

-639

.589

• 54^

•509

-477

-448

.423

.400

.380

3.00

•934

.851

-7«3

.725

-675

.631

-592

-558

.528

-501

-477

3.25

1. 112

1. 019

.941

-875

.818

.767

.722

.682

.646

.614

-585

3-50

1.306

1.204

1. 117

1.042

-975

.918

.867

.82c

-778

• 742

.707

3.75

I-SI7

1.404

1.307

1.223

1. 140

[.084

1.025

-973

.926

.882

.843

4.00

1-743

1.620

i-5!4

1. 421

i-338

1 .265

1. 199

1. 139

1.086

i-°37

-993

In Table 15 the proper proportions for the given loads have
been worked out.

TABLE 15.

Tons

Lbs.

TOOO

itk

2000

ifk

4000

5000

3
4

-4

I OOOO

12*

20000

19*

Hand Wheel. — Fig. 353 shows a drawing of a standard hand
wheel used for globe valves, etc., and in Table 16 is given the
usual proportions.

ELEMENTARY MACHINE DETAILS.

267

TABLE 16.

Dia.

1 4

T 7
is

If 1

1* \

Fig. 353.

Fig. 354-

Shaft Collars. — Fig. 354 shows a usual design for shaft
collars made in cast iron. Table 17 gives the correct proportions.

TABLE

17.

Bore.

1
4

Itt

7
to

_7_
16

4«

268 MECHANICAL DRAWING.

Frictional Coupling. — Fig. 354 shows three views of
Butler's frictional coupling. It is somewhat like the Sellers
coupling, except that it has neither bolts nor keys, the conical
bushes being held in position by round nuts threaded into the
muff. The conical bushes are split at the side, and when they
are in position on the shaft the split sides are at right angles
to each other; this arrangement allows a key-driver to be
introduced through one of these openings (after the nuts have
been removed) to drive out the other bush when it is desired
to remove the coupling from the shaft. The bushes are
guided into position by small dowel-pins which enter short
grooves provided for them inside the muff. The \" round
holes shown in top and bottom at the centre of the muff are
used to see when the ends of the shafts come together, for
then only will the coupling be in its proper position.

The threads on the lock-nuts should be that number per
inch used on a pipe whose outside diameter is nearest to the
outside diameter of the nut. The lock-nuts are screwed into
position by means of a spanner wrench having projecting
pieces which fit into the recesses shown in end elevation.
The taper of the conical bushes may be made j-" in 12" on
the diameter. The faces marked with small / are to be
finished.

The principal proportions of this coupling are as follows: ,

d = diameter of shaft;
D = diameter of muff = 2.2 $d;
' L = length of muff = 4^/.

ELEMENTARY MACHINE DETAILS.

269

270

MECHANICAL DRAWING.

Stuart's Clamp Coupling.— This coupling, shown in Fig.
355, differs from the Sellers coupling in having tapered

wedges instead of conical sleeves; these tapered wedges and
opposite halves of each end of the muff are bored to the size
of the shaft. Studs and nuts hold the wedges in place,
making, on the whole, a cheap and effective coupling without
the use of keys.

The principal dimensions of this coupling for various
diameters of shaft are given in the following proportions:
Let d = diameter of shaft;
D ~ diameter of muff;
L = length of muff.
Then for shafts from ij" to 2|" diameter
D = 3.2$d, L = 4.2$d;

for shafts from 2f " up

D = id, L = 4d.

ELEMENTARY MACHINE DETAILS.

271

272 MECHANICAL DRAWING.

Connecting-rods. — In steam and other engines the con-
necting-rod connects the rotating crank with the reciprocat-
ing cross-head.

There are many styles of connecting-rods, and various
methods are employed for taking up the wear of the brasses.
Figs. 356 and 357 show good examples of rods used in station-
ary, locomotive, and marine engines of the most modern
types.

Fig. 358 is the rod used by the Buckeye Engine Co. for
their " Tangye " type of engine. The crank end is solid, the
brasses are lined with babbitt, and adjustment for wear is had
by means of a tapered steel block and screws. The cross-
head end is called a strap end. The strap is firmly bound to
the end of the rod with a cotter-key and gib, which also con-
trols the adjustment for wear.

Fig. 359 has strap ends front and back. Keys are in-
serted between the straps and the rod to prevent the shear of
the strap-bolts. The construction of this rod and the method
employed to take up the wear are plainly shown in the figure.
The Erie City Iron Works use this rod on their stationary
engines.

Exercise 132. — Make the drawings as shown in Fig. 358.
(Scale 6" = 1 foot.)

Exercise 133. — Make the drawings as shown in Fig. 359.

ELEMENTARY MACHINE DETAILS.

273

rirt^rr

274

MECHANICAL DRAWING.

TABLE 18.

WIRE AND SHEET-METAL GAUGES COMPARED.

* .

si*

CO M

ilg.

^ 02

Roebling's and

Washburn

& Moen's

Gauge.

Stubs'

Steel Wire

Gauge.

(See also p. 29.)

British Imperial

Standard

Wire Gauge.

(Legal Standard

in Great Britain

since

March 1, 1884.)

U. S. Standard

Gauge for
Sheet and Plate
Iron and Steel.
(Legal Standard
since July 1, 1893.)

inch.

millim.

inch.

0000000

.49

.500

12.7

7/6
6/0
5/0

oooooo

.46

.464

11.78

.469

00000

.43

.432

10.97

.438

0000

.454

.46

.393

10.16

.406

4/0

000

.425

.40964

.362

.372

9.45

.375

3/0

.38

.3648

.331

.348

8.84

.344

2/0

.34

.32486

.307

.324

8.23

.313

.2893

.283

.227

7.62

.281

.284

.25763

.263

.219

.276

7.01

.266

259

.22942

.244

.212

.252

6.4

.25

.238

.20431

.225

.207

.232

5.89

.234

.22

.18194

.207

.204

.212

5.38

.219

.203

.16202

.192

.201

.192

4.88

.203

.18

.144-28

.177

.199

.176

4.47

.188

.165

.12849

.162

.197

.16

4.06

.172

.148

.11443

.148

.194

.144

3-66

.156

.134

.10189

.135

.191

.128

3.25

.141

.12

.09074

.12

.188

.116

2.95

.125

.109

.0S081

.105

.185

.104

2.64

.109

095

.07196

.092

.182

.092

2.34

.094

.083

.06408

.08

.180

.08

2.03

.078

072

.05707

.072

.178

.072

1.83

.07

.065

.05082

.063

.175

.064

1.63

.0625

.058

04526

.054

.172

.056

!.42

.0563

.049

0403

.047

.168

.048

1.22

.05

.042

.03589

.041

.164

.04

1.02

.0438

.035

.03196

.035

.161

.036

.91

.0375

.032

02846

.032

.157

.032

.81

.0344

.028

.02535

.028

.155

.028

.71

.0313

.025

.02257

.025

.153

.024

.61

.0281

.022

.0201

.023

.151

.022

.56

.025

.02

.0179

.02

.148

.02

.51

.0219

.018

.01594

.018

.146

.018

.46

.0188

.016

.01419

.017

.143

.0164

.42

.0172

.014

.01264

.016

.139

.0148

.38

.0156

.013

.01126

.015

.134

.0133

.35

.0141

.012

.01002

.014

.127

.0124

.31

.0125

.01

.00893

.0135

.120

.0116

.29

.0109

.009

.00795

.013

.115

.0108

.27

.0101

.008

.00708

.011

.112

.01

.25

.0094

.007

0063

.01

.110

.0092

.23

.0086

.005

.00561

.0095

.108

.0084

.21

.0078

004

.005

.009

.106

.0076

.19

.007

00445

.0085

.103

.0068

.17

.0066

.00396

.008

.101

.006

.15

,0063

.00353

.0075

.099

.0052

.13

.00314

.007

.097

.0048

.12

.095

.0044

.11

.092

.004

.10

.088

.0036

.09

.085

.0032

.08

.081

.0028

.07

.079

.0024

.06

.077

.002

.05

.075

.0016

.04

.072

.0012

.03

.069

.001

.025

■

ELEMENTARY MACHINE DESIGN.

275

DIFFERENT

Cent.

Fahr.

2IO°

4IO° .

221

430 .

256

493 •

26l

502 )
680 \

370

500

932

525

977

700

1292

800

1472

900

1657

1000

1832

IIOO

2012

1200

2192

1300

2372

1400

2552

1500

2732

1 600

2912

TABLE 19.

COLORS OF IRON CAUSED BY HEAT. (Pouillet.)
Color.
. . . Pale yellow.
. . . Dull yellow.
. . . Crimson.

. . . Violet, purple, and dull blue; between 261° C.
and 3700 C. it passes to bright blue, to sea-
green, and then disappears.
. . . Commences to be covered with a light coat-
ing of oxide; loses a good deal of its
hardness, becomes much more impressible
to the hammer, and can be twisted with
ease.
. Becomes nascent red.
. Sombre red.
, Nascent cherry.
. Cherry.
. Bright cherry.
. Dull orange.
. Bright orange.
. White.

. Brilliant white — welding heat.
Dazzling white.

TABLE 20.

TABLE OF DECIMAL EQUIVALENTS OF ONE INCH.

1/64

.015625

17/64

.265625

33/64

•515625

49/64

765625

1/32

.03125

9/32

.28125

17/32

•53125

25/32

78125

3/64

.046875

19/64

.296875

35/64

.546875

51/64

796875

1/16

.0625

5/i6

.3125

9/16

•5625

13/16

8125

5/64

.078125

21/64

.328125

37/64

.578125

53/64

828125

3/32

•09375

11/32

•34375

19/32

•59375

27/32

84375

7/64

•109375

23/64

•359375

39/64

.609375

55/64

859375

1/8

.125

3/8

•375

5/8

.625

7/8

875

9/64

. 140625

25/64

.390625

41/64

.640625

57/64

890625

5/32

.15625

13/32

.40625

21/32

•65625

29/32

90625

11/64

.171875

27/64

.421875

43/64

.671875

59/64

921875

3/i6

.1875

7/16

•4375

11/16

.6875

15/16

9375

13/64

.203125

29/64

.453125

45/64

.703125

61/64

953125

7/32

.21875

15/32

.46875

23/32

.71875

31/32

96875

15/64

234375

31/64

.484375

47/64

•734375

63/64

984375

1/4

.25

1/2

.50

3/4

• 75

276 MECHANICAL DRAWING.

TABLE 21.

CIRCUMFERNCES AND AREAS OF CIRCLES ADVANCING BY EIGHTHS.

Diam.

Circum.

Area.

Diam.

Circum.

Area.

Diam.

Circum.

Area.

1/64

.04909

.00019

2 11/16

8.4430

5.6727

6 5/8

20 813

34-472

1/32

.09818

.00077

3/4

8.6394

5 9396

3/4

21.206

35-785

, 3/64

.14726

.00173

13/16

8.8357

6.2126

7/8

21.598

37.122:

1/16

.19635

.00307

7/8

9.0321

6.4918

3/32

.29452

.00690

I5A6

9.2284

6.7771

21.991

38.485

1/8

.39270

.01227

1/8

22.384

' 39-87I

5/32

.49087

.01917

9.4248

7.0686

i/4

22.776

41.282

3A6

.58905

.02761

1/16

9. 62 1 1

7. 3662

3/8

23.169

42.718

7/32

.68722

•03758

1/8

9.8175

7.6699

1/2

23.562

44-179

1/4

.78540

.04909

3/^6

10.014

7.9798

5/8

23-955

45.664

9/32

.88357

.06213

1/4

10.210

8.2958

3/4

24-347

47-173

5/16

•98175

.07670

5/i6

10.407

8.6179

7/8

24.740

48.707

11/32

1.0799

.09281

3/8

10.603

8.9462

3/8

1. 1781

.11045

7/16

10 799

9.2806

25-133

50.265

13/32

1.2763

.12962

1/2

10.996

9.6211

1/8

25-525

51849

7/16

1-3744

.15033

9/16

11 . 192

9.9678

1/4

25.918

53456

is/32

1.4726

•17257

5/8

n.388

10.321

3/8

26 .311

55 088

1/2

1.5708

•19635

11/16

"■585

10.680

1/2

26.704

56.745

17/32

1 . 6690

.22166

3/4

11. 781

11.045

5/8

27.096

58.426

9/16

1. 7671

.24850

13/16

11.977

11. 416

3/4

27.489

60.132

*9/32

1.8653

.27688

7/8

12.174

"•793

7/8

27.882

61.862

5/8

1.9635

. 30680

15/16

12.370

12.177

21/32

2.0617

•33824

28.274

63.617

11/16

2.1598

.37122

12.566

1/8

28.667

65.307

23/32

2.2580

•40574

1/16

12.763

12.962

1/4

29 . 060

67.201

3/4

2.3562

.44179

1/8

12.959

13-364

3/8

29.452

69 . 029

25/32

2-4544

•47937

3/i6

13-155

13-772

1/2

29.845

70.882

13/16

2.5525

.51849

i/4

'3-352

14.186

5/8

30.238

72 . 760

27/32

2.6507

•559H

5A6

13-548

14.607

3/4

30.631

74.662

7/8

2.7489

.60132

3/8

13-744

15.033

7/8

31.023

76.58P

29/32

2.8471

.64504

7/16

i3-94i

15.466

15/16

2-9452

.69029

1/2

14-137

15.904

31.416

78.540

31/32

3.0434

•737o8

9/16

14-334

16.349

1/8

31.809

80.516

5/8

14-530

16.800

1/4-

32.201

82.516

3.1416

.7854

11/16

14 726

17-257

3/8

32-594

84-54I

1/16

3-3379

.8866

3/4

14-923

17.721

1/2

32.987

86.590

1/8

3-5343

.9940

13/16

15-119

18.190

5/8

33-379

88.664

3/i6

3-73o6

1.1075

7/8

15-315

18.665

3/4

33-772

90.763

x/4

3.9270

1.2272

15/16

15-512

19.147

7/8

34-i65

92.886

5/i6

41233

1-353°

3/8

4-3I97

1.4849

15.708

19.635

34-558

95-033

7/16

4.5160

1.6230

1/16

15-904

20.129

1/8

34-950

97 • 205

1/2

4.7124

1.7671

1/8

16.101

20.629

1/4

35-343

99.402

9/16

4.9087

1. 9175

3/16

16.297

2i.i35

3/8

35-736

101.62

5/8

5.1051

2.0739

x/4

16.493

21.648

1/2

36.128

103.87

Il/l6

5-30I4

2.2365

5/i6

16.690

22. 166

5/8

36.521

106.14

3/4

5-4978

2.4053

3/8

16.886

22.691

3/4

36.914

108.43

13/16

5.6941

2.5802

7/i6

17.082

23.221

7/8

37-3°6

110.75

7/8

5.8905

2.7612

1/2

17.279

23-758

15A6

6.0868

2.9483

9/16

17-475

24.301

37-699

113.10

5/8

17.671

24.850

1/8

38.092

"5-47

6.2832

3.1416

ji/i6

17.868

25.406

1/4

38.485

117.86

1/16

6.4795

3-34IO

3/4 £

18.064

25.967

3/8

38.877

120.28

1/8

6.6759

35466

13/16

18.261

26.535

1/2

39-270

122.72

3/16

6.8722

37583

7/8

18.457

27.109

5/8

39663

125.19

1/4

7.0686

3.9761

15/16

18.653

27.688

3/4

40.055

127.68

5/i6

7.2649

4.2000

7/8

40.449

130.19

3/8

7-4613

4.4301

18.850

82.274

7/i6

7.6576

4.4664

1/8

19.242

g9-465

1/2

7.8540

4.9087

1/4

I9.635

30.680

9/16

8.0503

5.I572

3/8

20.028

31-919

5/8

8.2467

5-4II9

1/2

20.420

33183

To find the weight of castings by the weight of pine patterns, multiply the
weight of the pattern by 12 for cast iron, 13 for brass, 19 for lead, 12.2 for tin,
14.4 for zinc, and the product is the weight of the casting.

COURSE II.

PROBLEMS IN
ADVANCED MECHANICAL DRAWING

INCLUDING

ISOMETRICAL DRAWING, ARCHITECTURAL DRAW-
ING, SHEET METAL DRAFTING, MACHINE DE-
TAILS, FREEHAND SKETCHING OF SMALL MA-
CHINE PARTS AND WORKING DRAWINGS OF
SAME.

277

COURSE II.
ADVANCED MECHANICAL DRAWING.

MINIMUM NUMBER OF PLATES AND MAXIMUM NUM-
BER OF HOURS ALLOWED TO COMPLETE EACH
DIVISION OF THE WORK.

FIRST SEMESTER. SIX HOURS PER WEEK.

Plate 22. Isometrical Drawing, to be handed in Sept. 24, 1909.

(14 hours.)
Plates 23 to 26 inclusive, Architectural Drawing, to be handed

in November 12, 1909. (42 hours.)
Plates 27 to 29 inclusive, Sheet Metal Drafting, to be handed

in December 17, 1909. (30 hours.)

SECOND SEMESTER. SIX HOURS PER WEEK.

Plate 30. Sheet Metal Drafting, to be handed in January 14,

1 910. (12 hours.)
Plates 31 to 1,1, inclusive, Machine Details, to be handed in

March 11, 1910. (42 hours.)
Plates 34 and 35, Freehand Sketches of small Machine parts

and Working drawings of same. (60 hours.)

Total, 200 hours.

279

280 MECHANICAL DRAWING.

Isometrical Drawing.

Plate 22. Make freehand sketches of (1) Library Book Trans-
ferring Shelves (2) Drafting Table, and (3) a twelve drawer
section of Drafting Room Lockers. These sketches are to
be made on an isometric paper pad with dimensions and title.
When sketches have been approved and signed, a finished
pencil working drawing is to be made.

Architectural Drawing.

Plate 23. Make finished pencil drawing of framing joints as shown
in Figs. 220-233 on Whatman's cold pressed white paper.
When approved and signed this plate is to be inked and
tinted in water colors.

Plate 24. Make finished pencil drawing of brick and stone work
shown in Figs. 234-240 on cream detail paper. WThen
pencil drawing has been approved and signed, it is to be
traced on cloth and blue printed.

Plate 26. Make finished pencil drawing of the examples of
Tuscan and Doric Orders of Architecture as shown in Figs.
243 and 244 on Whatman's cold pressed white paper. When
pencil drawing is approved and signed, it is to be inked
and the shaded and sectioned parts are to be tinted with a
light wash of India ink.

Plate 28. Make finished pencil drawing of the example of the
Ionic Order of Architecture as shown in Figs. 247 and 248 on
Whatman's cold pressed white paper. When the pencil
drawing is approved and signed, it is to be inked and the
sectioned parts are to be tinted with a light wash of India ink.

PROBLEMS IN ADVANCED MECHANICAL DRAWING. 281

Plate 25. Make drawing of the Classic Renaissance Letters,
Figs. 241 and 242. One alphabet 1" high and alphabets of
lesser height to fill one plate. Directions to be given by
Instructor. This plate may be made at odd hours during
the semester.

Sheet Metal Pattern Drawing.

Plate 29. Make pattern drawings of objects as shown in Figs.
276 to 288 inclusive, according to directions given on page
216.

Plate 30. Make pattern drawings of objects shown in Figs. 289
to 296 inclusive, according to directions given on page 218.

Plate 31. Make pattern drawings of articles shown in Figs. 297
to 310 inclusive, according to directions given in pages 223 to

Plate 32. Draw the developments of pipe elbows as given in
Figs. 311 to 314 according to directions given on page 226.

Machine Drawing.

Plate 33.

Prob. 1. Draw the U. S. standard or Sellers' V-threads,
Fig. 360, suitable for a screw 6" in diameter. Scale three times
full size.

See Table 1 for the value of p, the pitch of the screw, d is
the nominal diameter of the screw, dx the effective diameter of the
bolt, and n the number of threads per inch.

Prob. 2. Draw 2\ threads of the "Whitworth," or English
standard V-thread, Fig. 361, for 6" screw. Scale three times
full size.

282 MECHANICAL DRAWING.

Prob. 3. Draw the sectional outline of the square, knuckle
and buttress shown in Figs. 362 and 363, respectively. p=i"
Scale, full size.

Prob. 4. Draw the section of a pipe screw, Fig. 364, for a
wrought iron pipe 8" in diameter. Scale, three times full size.
See Table 2 for the number of threads per inch, the taper of the
screw and the thickness, t, of the pipe.

Prob. 5. Make drawings of the screw thread conventions
shown in Fig. 365. Scale, full size.

(1) is a right-hand double V-thread U. S. standard d=i".

(2) is a right-hand single V-thread U. S. standard d=\".

(3) is a right-hand single square thread U. S. standard

rf=i".

(4) is left-hand single V-thread U. S. standard d=i".

(5) is a right-hand double square thread U. S. standard
d=i".

(6) is a right-hand single V-thread U. S. standard d=%".
In the double thread the screw advances two pitches in each

revolution, therefore the inclination of the thread is equal to
the pitch. (6) is the standard convention used to represent
threads on the common sizes of bolts and nuts.

Prob. 6. Draw the projections of a hexagonal nut, Fig. 366,
for a bolt whose diameter d is equal to 1". Scale, full size.

F=i\d+\". D=FXi.iSS- H=d-

Construct the plan first. Draw the chamfer circle F and
circumscribe a hexagon about it with the 30°X6o° triangle and
T-square. Project elevation and end elevation from the plan.

Prob. 7. Draw the projections of a square nut, Fig. 367,
for a 1" bolt. Scale, full size.

As in the last problem draw the plan first and project the

PROBLEMS IN ADVANCED MECHANICAL DRAWING. 28

284 MECHANICAL DRAWING.

elevations from it. A square nut should never be shown in
elevation across the corners.

Prob. 8. Make drawings for 1" bolt with castle nut, Fig. 368.
Scale, full size.

The values of the letters in the figure are to be taken from
Table 3 which gives the standard proportions adopted by the
American Licensed Automobile Manufacturers. Use the same
proportions for drawing the chamfer curves on the elevations as
given for the U. S. standard nut. Make the saw cut in the head
.2d in width and the depth equal to ij times the width.

Prob. 9. Make drawings of the rectangular keys and their
connections shown in Fig. 370. Diameter of shaft D in No. 15
is equal to \" '. Scale, full size. Diameter of shaft in No. 16 is
equal to 2". Scale, 6"=i foot. Take the key dimensions from
Tables 5 and 6.

Prob. 10. Make drawings of the tension and compression
springs shown in Figs. 371 and 372. Scale, full size.

Fig. 372 is a compression spring and spindle for a boiler safety
valve. See model in drafting room.

Prob. ii. Make drawing of split pin shown in Fig. 369. Scale,
full size. Assume D = ^r, and d =.o$D + .13.

The split pin is made from half round wire which when pressed
into form gives a circular cross-section.

Selections from the following problems may be made to
Conveniently fill the space in Plate 34, allowing for title and bill
of material.

Plate 34.

Prob. i. Make drawing for a 2^-ton crane-hook, Fig. 379.
Scale, 6" = 1 foot. Find values for the different letters in Table 15.

PROBLEMS IN ADVANCED MECHANICAL DRAWING- 2S5

286 MECHANICAL DRAWING.

Prob. 2. Make the drawings of a cotter joint, Fig. 374. Scale,
full size. Taper of cotter is \" per foot.

Prob. 3. Make drawings of a nut wrench to dimensions
given in Fig. 375. Scale, full size. For other sizes of wrenches
see Table 7.

Prob. 5. Make drawings of a gib and cotter to dimensions
given in Fig. 327. Scale, 3"= 1 foot. S is the strap, B the brasses,
C the cotter, G the gib, R the connecting rod, and X the set screw.

Prob. 6. Draw the " Woodruff" key, Fig. 373, for a i\n
shaft. Take dimensions from Table 8.

Prob. 7. Draw the ball crank handle, Fig. 378, to the dimen-
sions given. Scale, full size.

Prob. 8. Make drawings of chain and link and narrow
shackle, Fig. 377. Scale, 4"=i foot. Take dimensions from
Table il

Prob. 9. Make drawing of taper pin, Fig. 64. Scale, full
size. Taper of pin is \" per foot. The finish curves at the end
are made with a radius equal to the diameter. The material
is steel.

Prob. 10. Make drawing of hand wheel, Fig. 65, outside
diameter 6". Scale, 6" = 1 foot. Take remaining dimensions
from Table 9.

Prob. ±i. Make drawings of a washer for a i|" bolt. Take
dimensions from Table 13. See Fig. 379.

Prob. 12. Make drawings of cast-iron flanges shown in Figs.
374 and 376 for a 1" bolt. Scale, 6"=i foot.

Prob. 13. Make working drawing of hand wheel, Fig. 381,
6" diameter. Scale, 6"=i foot.

Prob. 14. Make working drawing of shaft collar, Fig. 382;
for a 2" shaft. Scale, full size.

PROBLEMS IN ADVANCED MECHANICAL DRAWING. 287

Machine Detail Sketches.
Plates 35 and 36.

These plates are to contain certain machine parts to be applied
to the student by the instructor. Each object is to be sketched
in orthographic projection on an 8X10" sheet of cross-section
paper with a 4H pencil. Use only one side of the paper. Sketch
three views of each piece, viz., the elevation, plan, and right end
view. All dimensions, notes, title, and finish marks must be
neatly placed on the sketch.

Begin by drawing all the center lines for the front and end
elevations and the plan. Make size of sketch to suit size of paper.
Lines should be sketched very lightly and when sketch is approved
and signed in pencil, the lines may be strengthened.

Put on all dimension lines before measuring the object.
Measure with the two-foot rule and callipers. Callipers may be
borrowed from the Instructor.

Sufficient dimensions must be placed on the sketch to enable
the draftsman to make a working drawing for the pattern maker
without having recourse to the object, after the drawing is com-
menced.

When a sufficient number of sketches have been made to rill
one sheet of the usual size 15X20", working drawings are to be
made in finished pencil drawings. The finished pencil drawing
must carry all dimensions, notes, finish marks, title, bill of material,
and when approved and signed by the instructor it is to be traced
on tracing cloth and blue printed.

PRESENT PRACTICE IN DRAFTING ROOM
CONVENTIONS AND METHODS IN MAKING
PRACTICAL WORKING DRAWINGS.

Summary Report of an Investigation made by the Writer
with the Authority of the Armour Institute of
Technology. Chicago, III., into the Present Prac-
tice OF THE LEADING DRAFTSMEN IN THE UNITED STATES,
IN THE USE OF STANDARD CONVENTIONS AND METHODS
WHEN MAKING COMMERCIAL WORKING DRAWINGS.

A circular letter accompanied by a list of thirty-five questions
was submitted to two hundred leading firms in the United States
embracing nearly all kinds of engineering practice.

The returns have been exceedingly gratifying, and especially
so has been the spirit with which the " Questions" have been
received and answered.

Many requests have been received from chief draftsmen for
a copy of the returns.

The questions submitted and the answers received are given
somewhat in detail below.

290 MECHANICAL DRAWING.

Q. 1. Do you place complete information for the shop on the
pencil drawing, such as all dimensions, notes, title, bill of
material, scale, etc. ?

Complete information is placed on drawing before tracing. 57

Complete information is placed on tracing only 42

Principal dimensions and title only on pencil drawing 2

Draw directly on bond paper 10

Did not answer this question 10

Sometimes 7

Reasons given for making the pencil drawing complete:

To arrange notes. To save ime. The tracing is not usually
made by the draftsman who makes the pencil drawing.

Q. 2. Do you ever ink the pencil drawing?

Never ink the pencil drawing 91

Generally ink the pencil drawing 7

Sometimes ink the pencil drawing 8

Sometimes ink the pencil drawing and shellac it for shop use . 1

Use bond paper 10

Make pencil drawings on dull side of tracing cloth 2

Ink center lines of assembly drawing 1

Ink center lines of pencil drawings in red 2

Q. 3. Do you trace on cloth and blue print?

Always trace on cloth and blue print 102

Blue print from bond paper * 10

Blue print from bond paper occasionally 1

Sometimes make " Vandyke " prints for shop use 1

Sometimes use paper drawings in shop for jigs and fixtures . 1

Q. 4. Do you use blue prints entirely in the shop?

Use blue prints altogether in shop 105

Sometimes use pencil drawings or sketch 21

PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS. 291

Sometimes use sketches made with copying ink

Sometimes use prints from " Vandyke "

Use white prints mounted on cardboard and varnished

Use blue prints mounted on cardboard ,

Use sketches for rush work

Q. 5. When tracing do you use uniform wide object lines ?
Ever use shade lines?

Use uniform, thick object lines. Never use shade lines 100

Sometimes use shade lines 21

Use shade lines on small details 5

Always use shade lines 14

Experts in the use of shade lines may do so to make drawings

clear 1

Shade rounded parts 1

Q. 6. What kind of a center line do you use ?

Long dash, very narrow, and dot, thus : 42

Long dash and two dots, 29

Very fine continuous line, 19

Very fine dash line, long dashes, 8

Long dash and dot in red, 3

Continuous fine red line, 8

Long dash and three dots, 1

Long dash and two dots, thus: ] | 1

Q. 7. What kind of dimension line do you use ?

Continuous fine line, broken only for dimension ■ 52

Fine long dash line, ■ 32

Fine long dash line and dot, 13

Fine continuous red line, ■ — 8

F:ne continuous blue line, 4

Fine continuous green line, 1

292 MECHANICAL DRAWING.

Same character of line as center line, 2

Dotted line, - -- 1

Long dash and two dots, ■ 2

Heavy broken lines, 1

Q. 8. What style of lettering do you use ? Sloping ? Vertical ?
Free-hand? All capitals of uniform height? or capitals
and lower case ?

Free-hand sloping 52

Free-hand vertical 45

Free-hand capitals, Gothic, uniform height 61

Free-hand capitals, and lower case 40

All caps, initials slightly higher 5

Lettering left to option of draftsman 2

Mechanical lettering, all caps 3

Not particular, the neatest the draftsman can make free-
hand 4

Mechanical lettering, all caps, sloping 2

Give great latitude in lettering, only insist it be bold and neat 1

Roman, caps and lower case, free hand 2

Large letters i^ths, small -^ds and Jth 2

Q. 9. Are your titles and bills of material printed or lettered by
hand ?

Lettered by hand 79

Standard titles printed and filled in by hand 12

Bill of material table printed and lettered by hand 12

Lettered by hand, contemplate having them printed 1

B. of M. typewritten on separate sheet and blue printed... 8

Titles partly printed and filled in by hand 8

Use rubber stamp for standard title, fill in by hand 6

Standard title, bill of material lithographed on tracing

clem 8

PRESEXT PRACTICE IN DRAFTING ROOM CONVENTIONS. 293

Q. 10. Do you use a border line on drawings?

Always use border lines 97

Never use border lines 13

Use border lines on foundation plans, to send out

No border lines on detail drawings

Intend to discontinue the use of border lines

Border lines used only on design drawings

Only on drawings to be mounted on cardboard

Only used for trimming blue print 2

On assembly drawings only 1

Width of margins reported: 1", \" , f", J", and \" .

Q. 11. When hatch-lining sections, do you use uniform or
symbolic hatch lines ?

Standard symbolic lines 59

Uniform hatch lines for all materials . , 44

Shade section part with 4H pencil and note name of material 4

Symbolic hatch lines and add name of material 3

Uniform hatch lines for metal only 1

Uniform on details, symbolic on assembly drawings 5

Pencil hatch on tracings and note material other than cast

iron 1

Uniform hatch lines, sometimes solid shading 1

No uniform system 1

Sections tinted with water colors representing the metals.. 1

Q. 12. Is the pencil drawing preserved? Is the tracing
stored or do you make "Vandyke" prints for storing away?

Store tracings only 96

Pencil drawings preserved for a time 30

Pencil drawings preserved 13

White prints made and bound for reference 1

Tracings kept in office for reference, blue prints stored.... 9

" Vandyke " prints stored 1

294 MECHANICAL DRAWING.

Use "Vandyke" as substitute for tracing 2

Arrangement drawings preserved, detail drawings destroyed
after job is completed. Pencil drawings used for gasket

paper 1

Original pencil drawing inked and stored 1

Assembly drawings and layouts preserved 4

Patent office drawings preserved - 1

Tried " Vandyke " but found it unserviceable, tearing easily. 1

Q. 13. Do you use 6H grade of pencil for pencil drawings or
what?

6H 73

4H, mostly for figures and letters 52

5H 16

Ranging from 2H to 8H 53

Q. 14. Do you use plain orthographic projection for free-hand
sketches? Ever use perspective or isometrical drawing for
sketches ?

Plane orthographic 3d angle projection 99

Isometrical drawing for sketches 25

Perspective for sketches 1

Isometric for piping layouts and similar work 8

Perspective and isometric for catalogue work 2

Isometric sometimes 6

Never use free-hand sketches 6

One says, "When we run into other than orthographic, men are
too timid and not sure of themselves. In perspective drawings when
work is cylindrical, workmen get mixed up on center lines.

Q. 15. What sizes of sheets do you use for drawings?

9"Xi2" 13

12" X 18" 16

PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS. 295

l8"X24"... - - - 20

24"X36" - -- 19

There seems to be little uniformity in the sizes of shop drawings,
about 67 firms reporting different combinations. A few have no
system but simply make the size of sheet to suit the object to be
drawn.

Q. 16. Do you use red ink on tracings?

Never use red ink on tracings 57

Recently discarded the use of red ink 2

Use red ink for pattern figures 1

Use red ink for center and dimension lines 8

Use red ink for check marks 1

Use red ink for existing work on studies 1

Use red ink sometimes 2

Use red ink on occasions when it is desired to show old work

in red and new work in black (use carmine) 1

Use carmine for brick 1

Qs. 17 and 27. How indicate finished surfaces on drawings?
When finished all over? When "file finished," ground,
planed, bored, drilled, etc. ?

Finished surfaces indicated as in Fig. 1 65

Finished surfaces indicated as in Fig. 2 16

Finished surfaces indicated as in Fig. 3 8

Finished surfaces indicated as in Fig. 4 2

Finished surfaces indicated as in Fig. 5 2

Bound the surfaces with red lines 2

Bound the surfaces with dotted lines 2

Name the finish by note in full 68

Do not specify machinery method 6

(See drawing.)

296

MECHANICAL DRAWING.

Q. 18. Do you use horizontal or sloping lines for convention
in screw threads ?

Sloping lines, see Fig. 6 94

Horizontal lines, see Fig. 7 12

■#■

/=/A/.

/=/G. A

»«AHZ

Finish only third line from top

" L-f

^-^

Fig. 6.

^y ^

Fig. 7.

Fig. 8.

Fig. 9.

Horizontal lines, see Fig. 8
Both

Fig. 10.
... 13

Neither, but as shown in Fig. 9 1

Neither, but as shown in Fig. 10 1

PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS 2

Q. 19. When a large surface is in section do you hatch-line
around the edges only?

Hatch-line edges only 62

Sometimes

Hatch section all over

Do not use hatch lines; shade the whole surface with 4H

pencil ^

Usually show a broken surface line !

F/G.J/.

&GJ2.

Q. 20. Do you section keyways in hubs or show by invisible
lines ?

Section keyways as shown in Fig. 11 *,

Show key way by invisible lines, see Fig. 12 4o

Keyways in hubs left blank T

Q. 21. In dimensioning do you prefer to place the dimension
upon the piece or outside of it ?
Outside whenever possible o2

Upon the piece.

298 MECHANICAL DRAWING.

Both, according to size and shape of part 19

No rule „ 1

Commenting on placing dimensions outside of piece one says,
"It entails less confusion to workman." Another says: "So as to
make detail stand out."

Q. 22. Do you use feet and inches over 24 inches?

Yes 69

Use feet and inches over 36" 4

Use feet and inches over 24" on foundations and outlines . . 2

Use feet and inches over 48" 6

All inches ...... 21

For pulleys use inches up to 48" 1

Inches up to 10 feet 2

Start feet at 24" thus : 2—0" 2

Usually, but not always 2

Yes, except pitch diameters of gears, which are all given in

inches 2

Yes, except in boiler and sheet iron work 3

Use feet and inches over 12" 6

Inches up to 100" 3

Inches up to 60" 1

Q. 23. How do you indicate feet and inches? Thus 2 ft. 4",
or thus 2—4"?

2-4"— 97, 2"' 4"— 5,2 *T. 4"— 2, 2ft. 4"— 13. Both 2ft. 4"

and 2-4" — 1, 2FT. 4 in. — 1, 2' 4" — 8, 2-4" — 1.

Q. 24. Do you dimension the same part on more than one view ?

One view 94

More than one view as check 46

PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS. 299

Q. 25. When several parts of a drawing are identical would the
dimensioning of one part suffice for all, or would you repeat
the dimension on each part?

One part only 82

Would repeat or indicate by note 39

" Left to judgment of draftsman " 1

" When it is evident that several parts are identical the dimensioning
of one part would suffice, 'Would never leave room for doubt.'"

Q. 26. Do you write R for radius or rad. ? D. for diameter
or dia. ?

rad . . 35 Rad . . .47 R .... 32 rad. . . 1 r 3

dia . . 41 Dia . . 48 D. ... 15 d . . . . 3 dia ... 4
diam .... 1 Diam. ... 3 diam 5

Do not use R. or rad., dimension only 1

Q. 28. Do you always give number of threads per inch?
When you do how are they indicated ?
Only give number of threads when not standard 67

All others always indicate number of threads in a great variety of
ways. A few of the different styles of noting the threads are given
below :

}" — 10 Thr. 5THDS. per 1". 8thds. 4 threads per inch. Mach.
Screw 10-24, i\" XII, 16 P. RH. Vth. U. S. S. XVIII, i"-8-
U. S. S. i" TAP, 8 pitch, 3 th'd r. h. sq. double, 5"-i8
thds. r. h. own st'd io thds. per inch. For pipe tap thus
\" p.t., etc., etc.

Q. 29. How do you "Mark" a piece to indicate on the bill of
material ?

Number it on drawing and put a circle around it 34

300 . MECHANICAL DRAWING.

By name or letter ' 35

By pattern number 2

By symbol and number ; . . 14

Castings, I, II, III, Forgings, 1, 2, 3.

Q. 30. When a working drawing is fully dimensioned why
should the scale be placed on the drawing ?

For convenience of drafting room 25

Check against errors 11

Not necessary 18

Scale not placed on shop drawings 18

For convenience in calculations and planimeter work 1

To give an idea of over-all dimensions when these are not
given. " We never saw a drawing so fully dimensioned

as to warrant leaving off the scale " 2

" If a drawing is to scale the scale should be on the drawing, whether
it is needed or not."

" It gives every one interested a better conception of the proportions
of the piece, and there are frequently portions" of a design which do
not require a dimension for the shop to work to, and which it is
interesting to scale from an engineering point of view."

"To get approximate dimensions not given on drawing."

"Impractical to dimension all measurements for all classes of
work."

"Scale will tell at a glance, dimensions would have to be
scaled."

"To obtain an idea of relative size of parts without scaling the
drawings."

"To sketch on clearance." "To proportion changes." "When
erecting to measure over-all sizes."

" In case a dimension has been left off, the scale will help out."

"This is a question of opinion; some will not have the scale, others
insist on. it." "We always give the scale."

PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS. 301

"It is an immense help and time saver fn the drawing room."

11 Generally no reason. In our work we combine standard apparatus
by 'fudge' tracing, and it is convenient to know scale so all parts will
surely be to same scale."

"In discussing alterations, additions, clearances, etc., it is con-
venient to know the scale instantly."

"For convenience in drafting room. We often put an arbitrary
scale on with a reference letter indicating scale to draftsman."

"To give toolmaker an idea of the size of the finished piece."

"As an aid to the eye in reading."
Above are some of the reasons given for placing the scale on the

drawing. Below are given a few of the reasons why some do not

place the scale on the drawing.

" Scale should never be used in shop," says one.

"Not necessary. Sometimes drawing is made out of scale."

" Not advisable, on account of workmen getting into the habit of
working to scale instead of to the figures.''

"Know of no good reason at all."

"Believe it best to leave scale off."

" Should not. Drawing should never be scaled."

"Know of no good reason why it should be."

" Should not be given on drawing."

"Do not object if left off, not needed."

Q. 31. Do you use the glazed or dull side of tracing cloth?
Dull side... 66 Glazed side. 32 Both 4

"Dull side, because it lies flat better in drawers."

" Dull side, so that changes which may be necessary while work is
under construction, can be made easily in pencil and later in ink."

"Dull side so tracings may be checked in pencil."

"It prevents curling."

" Both, although the glazed side, when traced on lies better in the
drawer."

302 MECHANICAL DRAWING.

"We use cloth glazed on both sides, work on convex side, so that
shrinkage of ink will eliminate camber."

" Dull, except for U. S. Government, who requires the glazed side
to be used."

Q. 32. How do you place pattern numbers on castings?

Pattern number with symbol or letter is placed on or near
the piece, e.g., PATT.-D-478-C 36

This question was not happily stated : most answers gave " raised
letters cast on," while the question like all the others refers to the
marking of the drawing.

Q. 33. How do you note changes on a drawing?

On tracing with date 32

New tracing and new number 17

Put a circle around old figure and write new figure beside

it with date 8

Make new tracing OB 5

Red ink with date 8

Use rubber stamp " Revised" with date, and indicate changes

on record print 28

Use change card system 1

Special forms for purpose. Change made in a book with

date. New prints made to replace. In place at title

with draftsman's initials and date 8

Q. 34. Do you place dimensions to read from bottom and
right hand, or all to read from bottom, or how ?

Bottom and right hand . .. 103 From bottom only 2

No fixed rule 2

From R to L and bottom to top 1

PRESENT PRACTICE IN DRAFTING ROOM CONVENTIONS. 303

Q. 35. Do you always make a table to contain the bill of
material ?

Yes 49 No 25 Not always. . 5

Usually 1 Use separate bill 32

Bills on general drawings only. On details number is marked on
piece.

"No, but it is advisable to do so." "Have abandoned that
system."

INDEX.

PAGE

A. L. A. M. Standard Screw Threads 246

Angle, To Bisect an 19

Angle, To Construct an 15

Anti-friction Curve, "Schiele's " 50

Arched Window-Opening, To Draw an •. 53

Architectural Design 175

Architectural Drawing 162

Architectural Specifications 176

Arkansas Oil-stones 5

Ball Crank Handles 263

Baluster, To Draw a 53

Bills of Material 292, 303

Board, Drawing 1

Border Lines 293

Bow Instruments 2

Brass, Sheet of 6

Breaks, Conventional 61

Brickwork 166

Brilliant Points ic6

Buttress Thread 235

Celluloid, Sheet of Thin ^

Cement Work 185

Center Lines 60, 291

Chains 262

Cinquefoil Ornament, To Draw the 33

Circle, Arc of a, To Draw a Line Tangent to an 33

Circle, Arc of a, To Find the Center of an 32

Circle, To Construct the Involute of a 4;

Circle, To Draw an Arc of a, Tangent to a Straight Line and a Circle 37

Circle, To Draw an Arc of a, Tangent to Two Circles 36

Circle, To Draw an Arc of a, Tangent to Two Straight Lines 34

305

306 INDEX.

PAGE

Circle, To Draw a Right Line equal to Half the Circumference of a 31

Circle, To Draw a Tangent between Two 33

Circle, To Draw Tangents to Two 34

Circle, To Find the Length of an x\rc of a, Approximately 47

Circle, To Inscribe a, within a Triangle 35

Cissoid, To Draw the 49

Cistern 184

Closets V. . 193

Compass 2

Complete Information on Pencil Drawing 290

Connecting Rods 272

Conventional Breaks 61

Conventional Lines 60

Conventional Screw-threads 62

Conventions 56

Conventions, Shading 104

Cornice 190, 213

Cotter and Gib 25 7

Cotters ' 254

Coupling, Friction 268

Coupling, Stuart's Clamp 270

Crane Hooks 264

Cross-sections " 62

Curves, Irregular , 3

Cycloid, To Describe the 46

Dark Surfaces 104

Development of a Locomotive Gusset Sheet 97

Development of the Surface of a Cone 93

Development of the Surface of a Cylindrical Dome 96

Development of the Surface of a Right Cylinder 92

Development of the Surfaces of a Hexagonal Prism 90

Development Problems 155

Dihedral Angles 75

Dimensioning Drawings 297, 302

Dimension Lines 291

Direction, The, of the Rays of Light 105

Directions to Students 137

Dividers, Hair-Spring 2

Doors 195

Drafting-Room Conventions 289

Drawing-board 1

Drawing-pen 2

Drawing to Scale 12, 54

Drawings, S izes of Sheets 294

INDEX. 307

PAGE

Electric Wiring 208

Ellipse, Given an, to Find the Axes and Foci 43

Ellipse, To Describe an 38

Epicycloid, To Describe an Interior 50

Epicycloid, To Describe the 48

Equilateral Triangle, To Construct an 24

Examples of Working Drawings 120

Figuring and Lettering 66

Finished Parts of Working Drawings 122

Finish Indications 295

Flanges, Cast Iron 291

Floors 192

Framing Joints 164

Geometrical Drawing 16

Geometrical Drawing Problems 149

Glass-paper Pencil Sharpener 4

Gothic Letters 69

Grade of Pencils 294

Handles, Ball Crank 263

Hatch Lines 293

Heating 210

Heptagon, To Construct a 28

Hooks, Crane 264

Hyperbola, To Draw an 42

Hypocycloid, To Describe the 48

Ink Eraser 4

Inking the Pencil Drawing 290

Ink, Red 295

Inks 4

Instruments 2

Intersection Problems 156

Intersection, The, of a Cylinder with a Cone 93

Intersection, The, of a Plane with an Irregular Surface of Revolution 102

Intersection, The, of Two Cylinders 96

308 INDEX.

PAGE

Involute, of a Circle, To Construct the 45

Isometrical Cube 113

Isometrical Drawing 112

Isometrical Drawing, Direction of the Rays of Light in 114

Isometrical Drawing, Examples of 117

Isometrical Drawing of a Hollow Cube 116

Isometrical Drawing of a Two-armed Cross 115

Isometrical Problems 158

Isometrical Scale, The 114

Keys 249

Keys, Fixed 25 2

Keys, Flat 250

Keys, Round 25 1

Keys, Saddle 249

Keys, Sliding Leather 253

Keys, Sunk 250

Keys,- Woodruff 25 3

Key ways in Hubs 297

Knuckle Thread 235

Lathing. 185

Leads for Compass 13

Lettering 137- 147, 168, 214

Lettering and Figuring 64

Lettering, Style of 292

Line of Motion 60

Line of Section 60

Line of Shade 106

Line, To Divide a 21

Line, To Draw a, Parallel to Another 19

Lines„ « 291

Machine Details 228

Masonry Work 182

Mechanical Drawing and Elementary Machine Design 122

Model of the Co-ordinate Planes 8r

Moulding, The " Apophygee " 52

Moulding, The " Cavetto " or " Hollow " 5 r

Moulding, The " Cyma Recta " 51

Moulding, The " Echinus," " Quatrefoil," or " Ovolo" 52

IXDEX. 309

PAGE

Moulding, The " Cyma Reversa " 52

Moulding, The " Scotia " 51

Moulding, The " Torus " 52

Needles 6

Notation 8o

Notes on Drawings 302

Nut 240

Nut Wrench 259

Octagon, To Construct an 28

Orders of Architecture 171

Orthographic Projection , 74

Oval, To Construct an 43

Painting 202

Paper 2

Parabola, To Construct a 41

Pattern Numbers 302

Pencil 2

Pencil Drawings 293

Pencil Eraser 4

Pencil, To Sharpen the 8

Pen, Drawing 9

Pen, To Sharpen the Drawing 10

Pentagon, To Construct a 28

Perpendicular. To Erect a 17

Pipe Threads 236

Planes of Projection, The 75

Plastering 187

Plumbing . . 203

Polygon, To Construct a 26

Porches 190

Problems in Advanced Mechanical Drawing 277

Problems in Geometrical Drawing 149

Problems in Intersections i>6

Problems in Isometrical Drawing 158

Problems in Mechanical Drawing 134

Projection of the Helix as Applied to Screw-threads 99

Projection, The of Plane Surfaces 84

Projection, The, of Solids 90

3IO INDEX.

PAGE

Projection, The, of Straight Lines 82

Projection, The, of the Cone 93

Proportional, To Find a Mean, to Two Given Lines 31

Proportional, To Find a Third, to Two Given Lines 31

Proportional, To Find a Fourth, to Three Given Lines 32

Protractor 6

Quatrefoil, To Draw the „„.„.. 53

Rays of Light 104

Rays, Visual 104

Red Ink 295

Rhomboid, To Construct the 21

Right Angle, To Trisect a 24

Roman Letters 67

Roof 190

Scale Guard 6

Scale, Drawing to . . 12, 54

Scale on Drawings-. 300

Scale, To Construct a 55

Schiele's Curve, To Draw 50

Screw-threads, Conventional 62, 239, 296

Screw-threads, Regular 100

Screws 228

Section Lines 56

Section Lines, Standard 58

Shade Lines 297

Shade Lines and Shading 103

Shade, To, a Concave Cylindrical Surface no

Shade, To, the Elevation of a Sphere 108

Shade, To, a Right Cone no

Shade, To, a Right Cylinder 109

Shadows in

Sharpen Pen, To 10

Sharpen Pencil, To , 8

Sheet Brass 6

Sheet Celluloid 6

Sheet-metal Pattern Drafting . 216

Shingles 190

" Sibley College " Set of Instruments 2

" Sibley College " Set of Irregular Curves 3

INDEX. 3 II

PAGE

Sketches, Freehand 287

Source of Light 104

Spiral, To Describe the 44

Split Pins 248

Sponge Rubber - 5

Springs 260

Square Thread 235

Square, To Construct a 25

Standard Screw Threads 23 2

Stippling 100

Table, Decimal Equivalents 275

Table, Heat Colors 275

Table of A. L. A. M. Screw Threads 246

Table of Chains 262

Table of Circumferences and Areas of Circles 276

Table of Crane Hooks 266

Table of Flanges, Cast Iron 262

Table of Hand Wheels 267

Table of Shaft Collars 267

Table of Standard Screw Threads 244

Table of Taper Pins 249

Table of Washers 263

Table of Wire and Sheet-metal Gauges 274

Tacks 5

Taper Pins 248

Third Dihedral Angle 75

Tinting Brush 5

Tinting Saucer 5

Title, Standard 148

Title, The, of a Working Drawing 122

Titles 292

Tracing Cloth 6, 301

Trefoil, To Describe the 53

Triangles 3

Triangle, To Construct a 25

Triangular Scale 3

Triangulation 221

T-square 2

Type Specimens 70

United States Standard Screw Threads 232

Use of Compasses 1 3

Use of Dividers or Spacers. 13

312 INDEX.

PAGE

Use of Drawing- tward. . ........_.... i r

Use of Drawing-pen 9

Use of Instruments y

Use of Irregular Curves 14

Use of Pencil 8

Use of Protractor 14

Use of Scale 12

Use of Spring Blows 14

Use of Triangles n

Use of T-square . , 1 1

Visual Rays 104

Volute, To Describe the " Ionic " 45

Washers 263

Water-colors 5

Water Glass 5

Whitworth V Thread 233

Wire Gauges 274

Woodruff Keys 254

Working Drawings , 118, 159

Working Drawings, Examples of 119

Working Drawings, Method of Making 119

Working Drawing, What is a 119

Wrench 259

Writing-pen 6

676

**V \ V 'JV ,/ %■ '- *Hr / / %

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